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A stem-and-leaf plot with decimals 2020-04-02
From Renee:
I am an AP Statistics student who is reviewing for the exam.

On one of my review worksheets, we have to create a stem-and-leaf plot for values with 2 decimal places (i.e. 9.14, 8.14, 8.74, 8.77, 9.26, 8.1, 6.13, 3.1, 9.13, 7.26, and 4.74).

How would I make the stem-and-leaf plot for this? I've already searched your database and nothing popped up.

If you could help me, that would be great. Thank you!

Answered by Penny Nom.
The binomial distribution 2019-10-01
From PY:
An on-line game called ‘Shop Quiz’ is held by an e-commerce platform, from Monday to Friday every week. It consists of 8 multiple choice questions (MCQ) and each question has four options (A, B, C, D). Only one option is the correct answer. People who are able to correctly answer all 8 questions are winners and will be awarded a number of on-line shopping credits. Let X represent the number of questions that a person can answer correctly in a ‘Shop Quiz’.

1) Explain why Binomial distribution might NOT be a suitable distribution for the random variable X.

Mr. Saul likes playing the quiz, however, he is afraid that he might not have the necessary knowledge to answer the quiz questions. (The quiz questions cover a variety of topics including science, history, entertainment, sports and geography, etc.) Therefore, he tries to win the game by simply guessing the answers to each question.

Answered by Penny Nom.
Matched pairs 2017-12-13
From Lin:

Imagine you and your 4 study group partners are interested in whether all
those hours you spent together working on statistics problems for midterm
exam 2 actually helped your group's performance on that exam relative to its
performance on the first midterm exam. Suppose the first and second midterm
grades were as follows:
Is there sufficient evidence (at a = :05) to conclude that the group performed
better on midterm 2? Please provide all your calculations.

  midterm 1 midterm 2
A 25 28
B 20 19
C 15 21
D 16 25
E 20 22

Answered by Penny Nom.
A pie chart 2016-12-05
From vickie:
Determine the central angle needed to form a pie chart for the following housing characteristic data: 63% owner occupied, 27% renter occupied, and 10% vacant
Answered by Penny Nom.
The number of standard deviations 2014-06-15
From Dawn:
Suppose that, at a certain college, the average weight of all male students is 160 pounds with a standard deviation of 30 pounds. A certain male student weighs 145 pounds. Determine how many SD's his weight is above or below average.
Answered by Penny Nom.
Cumulative Frequency Math Question 2013-03-20
From Primadonna:


Please help me solve this question.

Thank you so much.

The cumulative frequency table below shows the length of time that 30 students spent text messaging on a weekend.

Minutes Used Cumulative Frequency
31-40 2
31-50 5
31-60 10
31-70 19
31-80 30

Which 10-minute interval contains the first quartile?

(1) 31–40

(2) 41–50

(3) 51–60

(4) 61–70

Answered by Penny Nom.
The range in grouped data 2012-08-27
From maria:
Question from maria, a student:

how to find range from group data.?i know that it is the difference between largest and smallest value.but confuse to find range of group data e.g

class interval frequency
0------5 6
5------10 7
10------15 9
15------20 4

Answered by Robert Dawson.
A normal distribution problem 2012-05-13
From Alysia:
The scores on a test taken by 1000 students are normally distributed with a mean of 66 and standard of deviation of 12. If the college wishes only the top 8% of people to get an A, what would the cutoff score be for the A's?
Answered by Penny Nom.
A pie chart 2012-05-01
From muhammad:
How can i construct a pie chart on the following of the combunation of students:- Sos 50, Crs 25, Eng 100, Iss 75, Geo 150, Hist 10
Answered by Penny Nom.
Expected value 2012-02-24
From Lara:
A life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old male for $350. According to the National Vital Statistics Report the probability that the male survives the year is 0.998734. Compute and interpret the expected value of this policy to the insurance company.
I'm very confused on how to do this. I assume x is the profit the insurance company makes in the year of $350 but beyond that I don't know what to do. Thanks.

Answered by Penny Nom.
The same mean but different ranges 2012-01-14
From swathi:
Frank and Frances work out at their local gym. the mean of their workout times is the same: 48 min. however, the range of Frank's workout times is 7 min, while the range of Frances'sworkout times is 16 min. explain how this is possible.
Answered by Penny Nom.
The average age of 300 cars 2011-11-22
From Jason:
I have 300 used cars built from 1970 to 1980, I would like to know the average age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?
Total built 50 56 30 10 30 25 64 9 12 14
Year built 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980


Answered by Penny Nom.
Sample Standard deviation 2011-03-16
From Iris:
Help please: me on this type of math problem I can get through step one after that I get lost. Maybe you can explain it to me in a easier way to get the correct results. I have read the examples, but I am still lost cannot move on until the next practice until I get this one

Sample standard deviation
The following are distances (in miles) traveled to the workplace by employees of a certain computer company.

15,29,32 28 18 28
Find the standard deviation of this sample of distances. Round your answer to at least two decimal places.

Answered by Penny Nom.
A normal distribution problem 2010-12-02
From Racquel:
I am stuck on this question. I am not sure if using the z score will help me get the answer I need. Here is the question?

The average length of time per week that students at this university spend on homework is normally distributed with a mean of 18 hours and a standard deviation of 3 hours. If Diane spends more time on homework each week than 75% of students, what is the minimum time she must spend?

Answered by Penny Nom.
t scores, z scores, standard scores and percentile ranks 2010-11-25
From Imogen:
I have an assignment that requires me to calculate the t scores, z scores, standard scores and percentile ranks of 3 children on a vocab task. I am struggling with how to calculate the correct T-scores for the children, my tutor has said that the sample has a mean of 50 and standard deviation of 10. So on a z- score of 2.0 (2 SD's from the mean) it would be 50 + 10+10 = T score of 70. However the Z- scores i have are not whole numbers so I am struggling with it, i have one that is 1.27 , another that is 0.47 and the last one is 0.80. If you could help me on how to calculate these to get T scores that would be great. Thanks.
Answered by Robert Dawson.
Standard deviation 2009-10-27
From Reggie:
After you have computed the standard deviation of a set of 40 scores, you discover that the lowest score is in error and should be even lower. Will correcting this error affect the standard deviation?
Answered by Penny Nom.
Airline overbooking 2009-09-03
From Nikita:
An airline company knows that 8% of it's passengers will not show up for their scheduled flights. A plane has 175 seats.

a) What is the probability that 10 passengers or fewer will not show up?

b) What is the probability that 10 to15 passengers will not show up?

c)What is the probability that exactly 10 passengers will not show up?

d) What is the probability that more than 19 passengers will not show up?

Answered by Robert Dawson.
Normal Distribution 2009-09-02
From Nikita:
Scores on a college exam are known to be normally distributed with a standard deviation of 20. If the top 3% have scores in excess of 200, what is the mean score?
Answered by Robert Dawson.
A normal distribution problem 2009-03-21
to qualify for security officers training recruits are tested for stress tolerance. The scores are normally distributed with mean of 62 and a standard deviation of 8.
a.) If only the top 15% of recruits are selected, find the cutoff score
b.) If a candidate is rendomly selected, what is the probability that his or her socre is at least 55?

Answered by Harley Weston.
Probability 2009-03-12
From jude:
) Assuming that the heights of boys in high school basketball are normally distributed with a mean of 70 inches and a std dev. of 2.5 inches, how many boys in a group of 100 are expected to be 75 inches tall.

2) Past records from a bank show that the probability of being approved in the written application for hire is 0.63. Then the probability of being approved by the interview committee is 0.85, given that the candidate has been approved on the written application. What is the probability that a person will be approved on both the written application and the interview?

Answered by Robert Dawson.
The variance 2009-02-09
From Ashley:
what is the varinace of these scoress 53,67,43,54,58,54,47,35,45,56,45,47,54
Answered by Harley Weston.
The range of a set of numbers 2008-11-19
From krista:
hi, i was working on a math problem for homework and it asked me to find the range out of these numbers: 1,15,16,16,19,25,27,28,28, can you help me?
Answered by Penny Nom.
Finding the Raw Score for a Mean of 0 and Standard Deviation of 1 2008-10-02
From Anita:
A variable Y has a distribution of mean of Y =80 and standard deviation of Y=36. Find the values of A and B for transforming y*=A +BY so that mean of y* =0 and standard deviation of y*=1.
Answered by Janice Cotcher.
Reading a Histogram 2008-09-05
From Bea:
From a histogram only, can you find the frequency per each increment of an interval?
Answered by Janice Cotcher.
Alpha level 2008-07-23
From anonymous:
What is the advantage of using an alpha level of .01 versus a level of .05, What is the disadvantage of using a smaller alpha level?
Answered by Janice Cotcher.
A pre-employment evaluation 2008-02-06
From lisa:
An employer gives a pre-employment evaluation to a large group of applicants. The scores are normally distributed with a mean of 154 and a standard deviation of 21. The employer wants to interview only those applicants who score in the top 15%. What should the cut off score be for the interviews?
Answered by Harley Weston.
The standard normal distribution 2007-12-29
Statistics texts state that in a normal distribution, 1 standard deviation covers 68%, 2SD 95% 3SD 99.7%. However, on looking at the tables for normal curve areas, the percentage for a z value of 1 is 84.13. 68 % of values are covered at a z value of 0.47. The discrepancies exist even for other values but are smaller. So why is the rule of thumb so different from the Table for Normal Curve areas?
Answered by Harley Weston.
A decision based on data 2007-12-04
From manny:
You have administered a standardized test of manual dexterity to two groups of 10 semi skilled workers. One of these two groups of workers will be employed by you to work in a warehouse with many fragile items. The higher the manual dexterity of a worker the less likelihood that worker will break significant inventory. Because of a unique contract you must hire all 10 employees from one of the two groups and none of the employees from the other.

You must decide which group to choose. Choose at least two measures of central tendency and at least one measure of dispersion for each group and use those to make your choice. Be sure to justify your choice with at least one page of discussion and analysis.

Answered by Penny Nom.
A t-test 2007-11-20
From Rachel:
I am wanting to use the t-test to find if temperature over a period of 5 days was significantly different to the mean temperature for that time of year. So i want to compare expected temps to actual temps. The problem is that because the expected temperature is the same for the 5 days it gives me a standard deviation of zero. Does this mean the t-test cannot be used because the f-test can't be calculated. If so is there an alternative test?
Answered by Harley Weston.
p-values and t-distributions 2007-11-13
From Don:
I have a t-test statistic of 1.28 and a degree of freedom of 6. I know the p-value is .248 I cannot figure out how to calculate that value. I have used software to get it but I want to know how to calculate it using the t-distribution table.
Answered by Harley Weston.
Stem & Leaf Plots 2007-11-02
From Jen:
Trying to help my Gr.4 son with his math and i am a little lost here are the stem and leaf plots..
Stem Leaves
4          02
3          1226699
2          011255789
1          33357899

Stem Leaves
2          00011111223334455
1          range566788899

Question - How are the ranges for the stem & leaf plots different ?

Answered by Penny Nom.
Sample variance and population variance 2007-09-22
From Willy:
I have a question in sample variance and population
my name is Willy
the question in the attached file...

Answered by Harley Weston.
Standard deviation 2007-09-05
From Ethan:
Okay I have a question about standard deviation. Can you tell me a five number set of data that will have a standard deviation f zero and how you know that?
Answered by Stephen la Rocque.
A statistics example 2007-08-02
From Claudia:
A particular employee arrives to work some time between 8:00 am - 8:30 am. Based on past experience the Company has determined that the employee is equally likely to arrive at any time between 8:00 am - 8:30 am.

On average, what time does the employee arrive?

What is the standard deviation of the time at which the employee arrives?

Find the probability that the employee arrives exactly at 8:12 am?

Find the probability that the employee arrives between 8:20 am - 8:25 am?

Answered by Har.
The difference between two dice 2007-06-02
From smiley:
Two standards dice are rolled. Determine the probability that the difference between the two numbers on the dice is 2
Answered by Penny Nom.
Types of variances 2007-05-08
From Latoay:
my teacher asked me to name two type of vairiance. i feel the answer is population and simple variance but i'm not sure. thank you
Answered by Stephen La Rocque.
Incremental standard deviation 2007-04-28
From Murtaza:
Hi In relation my question asked earlier, i would first like to thank you for the prompt reply. But it has not answered my query yet. Let me frame the problem again. I have a mean value for N data items. (note that i know N but i donot know the distinct N data item values) Now the (N+1)th data item comes in and i calculate the new mean. (incremental method for that is simple). How do i calculate the new standard deviation. The formula you gave me requires me to read the data items once and at the end of the pass i will have have the standard deviation. But i need the STDDEV values at intermediate stages as well. Is it possible ? Murtaza
Answered by Penny Nom.
All samples of size 3 2007-04-19
From Liz:
Consider the population of the first seven integers: 1, 2, 3, 4, 5, 6, and 7; N=7. For this population, mean = 2 and standard deviation = 2.
a. How many samples of size three can be extracted from this population (sampling without replacement)?
b. Form the complete set of samples of size three and for each sample, compute the sample mean and median.

Answered by Penny Nom.
A box-and-whisker plot with no whiskers 2007-04-18
From Paula:
Is it possible for a box-and-whisker plot to have no whiskers? 3 whiskers?
Answered by Penny Nom.
A hypothesis test 2007-04-09
From Katrina:
I have already tried to do this problem but im having a very had time with it. Can you please help me.

Glamour Magazine sponsored a survey of 2500 prospective brides and found that 60% of them spent less than $750 on their wedding gown. Use a 0.01 significance level to test the claim that less than 62% of brides spend less than $750 on their wedding gown. How are the results affected if it is learned that the responses were obtained from magazine readers who decided to respond to the survey through an Internet Web site?

Answered by Penny Nom.
A missing observation 2007-04-02
From destinee:
please help me my problem is 5,11,19,3,15,17,5,n find n given the following info.range:16 mode:5 median:8 mean:10 what the heck is the answer
Answered by Penny Nom.
Acceptance sampling 2007-03-29
From Katrina:
The Medassist Pharmaceutical Company recieves large shipments of asprin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is only one or none that doesnt meet the required specifications. If a particular shipment of thousands of asprin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?
Answered by Penny Nom.
Skewness 2007-03-16
From Lyndsey:
How do I calculate the skewness of a set of data?
Answered by Penny Nom.
Range in statistics 2007-02-28
From Steve:
I was wondering if the range is considered as a positive or negative number, or does it ignore such indications?
Answered by Penny Nom.
Standard deviation 2007-01-15
From Kayleigh:
After i have added up all the squared deviations what do i do???, what is meant by "divide by one less than the sample size"
Answered by Stephen La Rocque.
A statistics question 2007-01-07
From Rick:
For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa-St Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the 0.05 significance level, can we conclude that the guideline is still reasonable?
Answered by Penny Nom.
Standard deviation 2006-10-04
From Jennifer:
I was wondering how to figure out a standard deviation if you only have the mean of the data and no other information?
Answered by Stephen La Rocque.
The median 2006-09-26
From Sam:
How do you find the median in a group of numbers?
Answered by Stephen La Rocque and Penny Nom.
The coefficient of variation 2006-05-20
From Glenn:
What is the correct formula for coefficient of variation for a binomial distribution?
Answered by Penny Nom.
Absolute Value vs. Standard Deviation ? 2006-04-24
From Sonia:
Why we don't just take the average of the absolute value of difference scores (use the mean deviation) to describe variability instead of calculating the standard deviation?
Answered by Claude Tardif.
A manufacturer of cotton pins 2006-03-20
From Nirmal:
A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity?
Answered by Penny Nom.
Outliers in a box and whisker plot 2006-02-19
From A student:
i need help on determining if their is an outlier...i know how to find the median and the lower quartile and the upper quartile..but i don't understand about the outliers....please tell me if their is an outlier in this problem....the numbers are...63,88,89,89,95,98,99,99,100,100
Answered by Penny Nom.
Another normal distribution problem 2006-02-18
From Mary:
Assume that blood pressure readings are normally distributed with a mean of 120 and standard deviation of 8. A researcher wishes to select people for a study but wants to exclude the top and bottom 10 percent. What would be the upper & lower readings to qualify people to participate in the study?
Answered by Penny Nom.
Broken-line graphs and histograms 2006-02-16
From George:

1. What is the main difference between a broken-line graph and a histogram? Both represent continuous variables.

2. What is the correct way to read a multiplication array: x-axis first and then y-axis, other way around or it doesn't matter?

Answered by Penny Nom.
A normal distribution problem 2006-02-15
From Mary:
In a certain normal distribution, find the mean when the standard deviation is 5 and 5.48% of the area lies to the left of 78.
Answered by Penny Nom.
The median 2006-01-27
From Wael:
" median"; what does it mean and how do we calculate it?
Answered by Penny Nom.
A confidence interval 2006-01-21
From Jonathan:

I am attempting to calculate how my confidence interval will widen at the 95% confidence level if my response universe increases from 100 to 150 or to 200.

There is a universe of 54,000. I take a 5% sample for a test universe of 2,700

If my "yes" universe is 100, at the 95% confidence level, what is my +/- range? (i.e +/- 3? +/-5?)

Historically, 6.6% of the 2,700 you say "yes". I am trying to determine how the confidence interval would change if the number of "yes" responders increased to 150 or to 200.

Answered by Penny Nom.
Mean and average 2005-12-22
From Jerry:
This is just a question from a degreed engineer that has a "understanding" problem. please go to http://www.metrika.com/3medical/hemoglobin-m.html

At the end of the page they talk about "mean" vrs "average" there does appear to be a difference. What is it?

Answered by Harley Weston.
A sample size estimation 2005-12-03
From Ivonne:
I have to do a research about the behavior of library users. We are going to apply a survey to a population of 1280 students (Management an Economics students) but of course we have to do it to a sample....I need to know the size of my sample.
Answered by Penny Nom.
Coefficient of variation 2005-10-19
From Jan:
I am currently teaching the coefficient of variation and am wondering if there are some guidelines as to the interpretation of this statistic. I understand that it measures the variation in a variable relative to the mean - but what is the cut off for "too much" variation expressed in this way???
Answered by Andrei Volodin and Penny Nom.
The range of a data set 2005-10-04
From Carmen:
What is the range of this data? 36,64,37,45,53,60.
Answered by Penny Nom.
Sample variance 2005-08-17
From Rosalie:
To give an unbiased estimate of the population variance, the denominator of the sample variance should be (n-1) instead of n. I tried to convince myself by comparing the population variance and sample variance (with denominator n and n-1):
Answered by Penny Nom.
A normal distribution problem 2005-08-08
From Brad:
The life of a toy is normally distributed. Suppose 92.51% of the items lives exceeding 2,160 hours and 3.92% have lives exceeding 17,040 hours. Find the mean and the standard deviation.
Answered by Penny Nom.
Standard deviation 2005-01-02
From Urial:
Find the standard deviation of the given data set
To get the best deal for CD dealer, Jessica called eight appliance stores and asked the cast of a specific model. The prices she quoted are listed below.

$300, $203, $272, $332, $440, $119, $129,$254

Answered by Penny Nom.
Computing confidence intervals 2004-11-26
From Christie:
I was given a question with N=100, sample proportion is 0.1- compute the 95% confidence interval for P? I have tried this several ways but do not know how to do without means, standard deviations, standard error of the mean? I asked my teacher and she said I have all the info I need. Can you help????
Answered by Penny Nom.
A standard deviation test 2004-11-09
From Karen:
How do you compare to see if a sample standard deviation is different than the population standard deviation? I know how to compare means, but not standard deviations.
Answered by Penny Nom.
Incremental variance 2004-09-23
From Carlos:
I must keep statistical data (mean and variance) in 3 granularity levels depending on the age of the data (daily for older than 1 year, hourly for older than 1 month and quarter-hour for older than 1 day). How can I calculate the resulting variance from a set of variances previously calculated supposing I have the count and mean for each member of the set?
Answered by Andrei Volodin and Penny Nom.
Percentiles 2004-08-15
From Gary:
Table 1 Selected percentiles for family income in the US in 1992 1 $1,300 10 $10,200 25 $20,100 50 $36,800 75 $58,100 90 $85,000 99 $151,800

Q. The percentage of families in Table 1 with incomes below $58,100 was about?

Answered by Penny Nom.
A probability question 2004-08-15
From Gary:
In a law school class, the entering students averaged about 160 on the last LSAT; the standard deviation was about 8. The historgram of the lLSAT scores follwed the normal curve reasonable well.

Q. About what percentage of the class scored below 166?

Q. One student was 0.5 above average on the last LSAT, about what percentage of the students had lower scores than he did?

Answered by Penny Nom.
The p-value 2004-07-25
From Kathy:
Ms. Lisa Monnin is the budget director for the New Process Company. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?

Having problems finding the p-value & unsure of the formula. Kathy

Answered by Penny Nom.
Chi-Squared 2004-05-05
From Gillian:
Answered by Penny Nom.
Replacement times for TV sets? 2004-03-31
From Barb:
Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e
Answered by Andrei Volodin and Penny Nom.
A least squares line 2003-11-09
From Michelle:
Hooke's Law asserts that the magnitude of the force required to hold a spring is a linear function of the extension e of the spring. That is, f = e0 + ke where k and e0 are constants depending only on the spring. The following data was collected for a spring;

e: 9 , 11 , 12 , 16 , 19
f : 33 , 38 , 43 , 54 , 61

FIND the least square line f= B0 + B1x approximating this data and use it to approximate k.
Answered by Penny Nom.

X bar 2003-11-04
From mary:
Remind me what this means:


Answered by Andrei Volodin.
Means 2003-10-28
From Abdu:


The average of the 8 numbers listed above is 88. Of the following which pair of numbers could be removed from the list without changing the average.

A. 80 and 97
B. 80 and 98
C. 84 and 92
D. 84 and 97
E. 85 and 92

Answered by Andrei Volodin and Penny Nom.
The mean house price 2003-09-10
From Carol:

I have to find the mean from the following example:

Price Range £000 No of Houses
55 and under 60 3
60 and under 65 6
65 and under 70 13
70 and under 80 21
80 and under 100 15
100 and under 130 7
130 upwards 1

I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated.

Answered by Penny Nom.
E(X + Y) and V(X + Y) 2003-07-10
From Reuben:

I'm a teacher trying to find a way to make some stats work from first principles. The topic is expectation algebra and it is for the top age level in high school.

By using a set of data I can show how the mean is the same as the expected value ie 2,2,3,4,4 is 15 / 5 = 3 also, 2x0.4+3x0.2+4x0.4=3. I can also show this to work for the variance in the same style but using Sum(x-mean)2/n and the Var(X) version of squaring x then multiplying by the probability ( all this for random independant samples).

Now comes the tricky bit.....when I try to show E(X+Y) = E(X) + E(Y) from setting up two data sets I get it to work only if I add each item from X to each item from Y. However, I can't get it to work for V(X+Y)=V(X) + V(Y) from two sets of data.

There must be something missing in my knowledge of how the sets are required to add together or my knowledge of expectation algebra. I am familiar with proofs but still want to show my students that the basic formulae work from groups of data whether done the long way or by use of formulae. Can you help please?

Answered by Penny Nom.
The effectiveness of a drug 2003-04-22
From A student:
A certain drug is found to be effective 80% of the time. Find the probability of successful treatment in two out of four cases.
Answered by Andrei Volodin.
Incremental standard deviation 2003-04-12
From Carlos:
I need to calculate the standard deviation for a group of data, but I don't know in advance what is the mean. Is there a way to adjust the STDV for each datum without keeping all of the previous values? This is needed basicaly for performance, so I won't need to read twice the same data (spend processing time) nor save the previous values (spend memory).
Answered by Andrei Volodin and Penny Nom.
Mean and median 2003-01-04
From Jan:

I have a question re: mean and median. I know what the difference is but just need some clarification on when you would use the mean and when you would use the median. Isn't it the case that with a skewed distribution the average (mean) would be higher or lower than the median, but with a normal distribution they would be very similar values?

If you have any examples to help explain this that would be greatly appreciated.

I am a teacher (of sorts!) and the person who is asking me the question is actually my boss!

Answered by Penny Nom.
Variance 2002-10-29
From Ade:
I am trying to solve a standard deviation question, I have 30 data points to use, should I group the data before solving for variance or should I just use the raw data.
Answered by Andrei Volodin.
Statistics 2002-10-11
From Ed:
Suppose 25 percent of all U.S. workers belong to a labor union. What is the probability that in a random sample of 100 U.S. workers, at least 20 percent will belong to a labor union?
Answered by Claude Tardif.
Mean, median and mode 2002-09-08
From Ramona:
  1. How do you calculate the mean, median, and mode?

  2. what are each of their definitions?

Answered by Leeanne Boehm.
On which assignment did I do better 2002-05-17
From Denise:
I have 2 writing assignments in class. The first assignment, which had a mean of 10 and a standard deviation of 2, I got a score of 12. The second assignment had a mean of 18 and an s.d. of 3, I got a 21. I need to know which assignment did I do better, relative to my classmates?
Answered by Andrei Volodin.
Day care 2002-05-13
From Sonam:
In many familes, both parents work. as a result, there is increasing need for day care. data was collected; and in one year in Canada, approximately 32% of children aged 0 to 11 years were in day care for at least 20h per week.

(a) what is the probability, in a random poll of 60 children form the age of 0 to 11, that more than 15 children are in day care at least 20 h per week? nearest tenth of one %

P(children are in daycare at least 20h)= 60/60C14 = to the answer

(b) what is the probability, in a random pool of 60 children that fewer than 20 are in day care at least 20 h per week?

P= 20/60= 33.3% stay in day care for 20h per week,

I dont know if these answers are right please help me out.

Answered by Andrei Volodin.
The Dugout, Don's Basement, Cd Corner,... 2002-04-30
From A student:
The Dugout, Don's Basement, Cd Corner, Harry's Deli, Bill's Software, Anne's Footwear, and Joanne's House cleaning.

The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and mode are both $70.

The certificate from The Dugout is worth the most and the one from Joanne House cleaning is worth the least.

The total value of the gift certificates from CD Corner, Harry's Deli, and Anne's Footwear is $270, but Anne's Footwear certificate is worth $50 more than the one from Harry's Deli. The Cd Corner gift certificate is equivalent to the mean for this group of three.

What is the value of the gift certificates from each store?

Answered by Penny Nom.
Range of values for standard deviation 2002-03-22
From Susan:
What is the range of values for standard deviation? Is it between 0 and +3? Is it between +1 and +3?
Answered by Andrei Volodin.
Testing a hypothesis 2002-03-14
From A student:
A large distriutor of cosmetics has kept his outstanding accounts receivable to a mean age of 18 days over the past year. This average is considered a standard by which to measure the efficiency of the credit and collections department. Management wishes to check if receivables in the current month is over standard and will do this at a significance level of 0.50. A random sample of 100 accounts yields an average of 20 days with a standard deviation of 9 days. what should management conclude?
Answered by Andrei Volodin.
The median with ties 2002-02-27
From Marcel:
What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median.
Answered by Harley Wston.
Linear regression 2002-01-16
From Murray:
If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]-m*x[m]-b) is at its absolute minimum.
Answered by Harley Weston.
Cinderella clothes 2001-12-11
From A student:
If cinderella clothes, inc. has determined that 0.5% of all incoming phone calls involve complaints, what is the probability that in 200 incoming calls there are more than one complaint?
Answered by Andrei Volodin.
Box and Whisker plots 2001-11-19
From Rod:
In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect.

My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not?

Answered by Penny Nom.
A sample size problem 2001-10-28
From Charles:
The U.S Transportation Dept. will randomly sample traffic reports to estimate the proportion of accidents involving people over the age of 70. The Dept. has no advance estimate of this proportion. how many reports should the dept select to be atleast 97% confident that the estimate is within .01 of the true proportion?
Answered by Harley Weston.
Column doesn't add up to 100% 2001-10-17
From A student:
why don't some tables I'm studying in a column add up to 100%? Example: N=338, but responses to questions asked in survey I'm studying equal of 24.3, 9.8, 43.8, DON'T add up to 100%. I'm assuming that some people surveyed out of the 338 didn't bother responding, but is there another problem related to proportion or ratio being used, but improperly labeled on graph?. Note at bottom of table says: "number in parenthesis are numbers of cases" and 338 was in parentheses. I'm lost.
Answered by Penny Nom.
Ciefficient of variation 2001-09-23
From Carmen:
I have a question from my OAC finite class. I've come across a problem with the coefficient of variation. I have taught my students that there are no units for coefficient of variation and it can be expressed as a percent. So, for example, a set of data with mean of 5 and standard deviation of 100 would have a CV of 5%. But what happens in this situation: the mean is 4meters and the standard deviation is 0.7mm. Is the CV 1.75% or 0.00175% or 0.0175%? I've had some students change leave the units as is, change them both to mm or change them both to meters...so which is it and why?
Answered by Penny Nom.
Margin of error 2001-07-13
From Jim:
If a survey was completed by four different groups of people as indicated below what would the over-all margin of error be for this survey given the fact that the number of people in each group were different?
Group   # polled   Margin of error 
A.           779           +/- 4% 
B.           315           +/- 7% 
C.           323           +/- 6% 
D.           254           +/- 9% 

Answered by Andrei Volodin.
Comparing means and standard deviations 2001-07-11
From Shelly:
Is there a way to compare means and standard deviations that come from different size samples? Is there an equation that can normalize sample size?
Answered by Andrei Volodin.
A confidence interval 2001-06-28
From Murray:
An investigator wants to find out of there are any difference in "skills" between full and part time students. Records show the following:
Student            Mean Score         Std Dev        Number
----------      -----------------     ----------     -----------
Full time              83                   12          45
Part time               70                   15          55
Compute a 95% confidence interval for the difference in mean scores.

Answered by Andrei Volodin.
SPRT 2001-05-24
From A researcher:
I have a medical-pharmaceutical study that says:

SPRT (something to do with Secuential and Truncated).

Do You know what it means S.P.R.T. and what it is?

Answered by Ejaz Ahmed and Penny Nom.
A confidence interval 2001-04-26
From Kim:
A poll asked 1528 adults if they were in favor of the death penalty, 1238 said yes, find 99% confidence level for percent of all adult who are in favor of the death penalty.
Answered by Andrei Volodin.
Expected value 2001-04-24
From Cindy:
A game consists of rolling a single fair die. If a number great than 4 is rolled you win the number of dollars showing on the die. If any other number is rolled, you receive $1.00. What is the expected value of this game?
Answered by Andrei Volodin.
Leukemia 2001-04-15
From Don:
Assume: Leukemia occurs at an incidence of 1 in 10,000.

Benzene is a known carcinogen which causes Leukemia and has been found in toxic levels in the homes of a community of 1200 people.

Question: How many cases of Leukemia would be necessary to reject the null hypothesis. That is, to suggest that statistically, the cases are more likely due to benzene exposure rather than chance.

Answered by Chris Fisher and Penny Nom.
Stem-and-leaf plot 2001-03-29
From Kelly:
I'm tutoring my 5th grade nephew, and he needs to correct test questions regarding a stem - and - leaf plot. He left his book at school and I'm not familiar with the term. Can you explain it to me so that I can help him?
Answered by Penny Nom.
What is the difference between Mean and Average? 2000-12-13
From Julie:
What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower)
Answered by Patrick Maidorn and Penny Nom.
Expected number 2000-11-02
From James:
1)There are 40,25,50 students in the traditional,reformed,and reformed traditional Calculas sections taught by three teachers. On one fine day the three sections congregate together to watch the NOVA video tape on Fermat's Last Theorem.

a) A student is randomly selected from he crowed of students.What is the expected number of students in the same section of this student?

****this question which i did not have any idea to do as follow for the part b
b) If one of the three teachers is selected at random, what is the expected number of students taught by is teacher?

Answered by Harley Weston.
Mode 2000-09-22
From James Barton:
I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others.
Answered by Claue Tardif and Harley Weston.
Central Limit Theorem and Law of Large Numbers 2000-06-26
From Jonathan Yam:
The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed. The Law of Large Number states that when sample size tends to infinity, the sample mean equals to population mean. Is the two statements contradictory?
Answered by Paul Betts and Harley Weston.
Probability and odds 2000-05-05
From Leah:
The chances of rain on friday, saturday, and sunday are 20%, 30%, and 50% respectively. what are the odds it will rain all three days?
Answered by Harley Weston.
An expected value 2000-04-24
From Carl Pride:
Suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent.


What is the expected number of students who will pass??

Answered by Harley Weston.
Sample variance 2000-04-16
From Jonathan Freeman:
I was just reading your article entitled "A Note on Standard Deviation" I'm now teaching a unit on s.d. and my students were wondering why one uses a denominator of n for a population and n-1 for a sample. I saw in your article that this is because "[the quantity] tends to underestimate sigma... and other technical reasons." To which my students again asked... "Why?" Could you please elaborate a bit on the "other technical reasons" perhaps in terms a high school senior (or their teacher...) could understand?
Answered by Harley Weston.
Box and whisker plots 2000-03-09
From Brett Blake:
Do you have any information on Box and whisker graphs?
Answered by Harley Weston.
Bar graphs and histograms 2000-01-11
From Raeluck:
What is the difference between a bar graph and a histogram?
Answered by Harley Weston.
Absolute value 1999-12-29
From Alex Waller:
What are some practical applications for absolute value?
Answered by Harley Weston.
.400 in Baseball 1999-12-15
From Nieve Nielson:
I have several questions to ask about the probability of getting a .400 in baseball:
  1. What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?

  2. What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind:

  3. Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?

Answered by Chris Fisher.
Mean, median and mode 1999-12-07
From J William Morning:
Using the data values 2,2,10,6,5, determine the median, mode and mean.
Answered by Penny Nom.
Estimating the population mean 1999-11-13
From John Barekman:
Statitistics: Estimating the population mean when the standard deviation is known:

I am not sure which n to use in the formula for the confidence interval equation:

x +/- z*(standard deviation/sqrt(n))

If we have data of ten people, and if we have the data of ten sets of ten people each, what is the difference in the n that we use? What is the difference between the standard deviation and the standard error? Are we using the number of sampling means or just the number of samples?
Answered by Harley Weston.

Body part measurements 1999-11-10
From V Bailey:
I am a kindergarten teacher and mother of a 6th grader who wants to do a science project on the correlations of body part measurements. We heard this on the radio and it sparked our interest, but now I cannot find any information about it. Examples are: your height is supposed to equal the distance from fingertip to fingertip when your arms are outstretched. Your foot size is supposed to equal the distance from your wrist to your elbow.

Please help me find more information on this topic.
Answered by Penny Nom.

Linear models 1999-11-09
From Helen Moreno:
What is a linear model?
Answered by Harley Weston.
Predictions 1999-09-22
From Joesph Dana:
How do u find the results of an unbiased sample of 100 students that are shown on the table. For example the school has a total of 1,150 students prdict how many students would chose cereal(46) pancakes(15) eggs(20) and sandwich(19)
Answered by Haeley Weston.
Stem and Leaf Plot 1999-09-14
From Jeanette Sovick:
My 5th grade son brought home a math paper, the title of which reads, Reading Stem-and-Leaf Plots...can you explain this so I can explain it to him...There is no book, his teacher just sent this practice sheet home for him to complete and I have no clue!
Answered by Penny Nom.
Standard Deviation 1999-07-11
From Anthony Fama:
I have seen several answers to this question: If one standard deviation represents 68% of the population, what does two, three, four and five sigma [std deviation] represent? As stated, I have seen several different answers and thus, the impetus for my question.
Answered by Harley Weston.
Probability and Statistics 1999-03-25
From Karrie Waller:
Hi my name is Karrie and I am an elementary ed. student at Florida State University in Tallahassee, Florida. I am doing a report on how children learn probability and statistics. I am having trouble locating information that will tell me specifically how students learn. I am wondering if you can answer this question for me or direct me in the right direction.
Answered by Jack LeSage.
Fitting a Curve 1999-01-19
From Kirk:
Hello my name is Kirk from Scarborough, Ontario.

I have been out of a formal education system for thirty years. I program microcontrollers in my spare time. I have built a temperature sensing device ready to go but, thermistors are very non-linear. I do know that there is a way to calculate the input condition of the thermistor and display the correct temperature in degrees C. I am sending a file to show my progression so far.
Answered by Harley Weston.

Random 1998-09-15
From Hugh Ballantyne:
I am an occasional teacher.
Here is my question:
Does the word "random" have a technical meaning in mathematics?

Answered by Harley Weston.
Graph Distortion 1998-02-19
From Dana Steffan:
What exactly is graph distortion? I have to explain it for a project and I can't seem to find anything on it.
Answered by Penny Nom.
Histograms. 1997-09-26
From David Wilson:
I need some help to teach my daughter the functions and the techniques involved in solving histograms. She is in the 7th grade and is in a prealgebra class.

She was give these as homework, however there is no section in her book explaining what a histogram is or how to solve them.
Answered by Penny Nom.

The normal distribution. 1997-03-21
From Donna D.Hall:
I am looking for a proof for the normal distribution.

I suppose "proof" was not a good choice of words. What I am looking for is a way to "derive" the normal distribution in simple terms so that the most average teenager can see the logic. Can you help me?
Answered by Harley Weston.

What is the variance of the difference of two binomials? 1996-02-08
From Chris Johnson:
My co-workers and I have come up with different estimates of the z-statistic, and are in particular disagreement over the calculation of Variance for this problem. I am trying to find out, with a five percent level of significance, whether the new form yields a higher rate of return than the old form. Any thoughts, comments, or solutions?
Answered by Harley Weston.



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