







Sample variance 
20100125 

From shodhan: A series of 100 measurements of a physical quantity have been made that show a random fluctions characterized by a sample variance of 2% of teh mean value. If the series is lengthed to 1000 measurements made under the same conditions, estimates the sample variance of the larger set of data. Answered by Robert Dawson. 





The variance 
20090209 

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. 





Sample variance: inches to centimeters 
20080922 

From Anita: The average height of a sample of basketball players is 6 feet, 2 inches or 74 inches.
The standard deviation of this sample of players is 4 inches. If each person's height were to be multiplied by 2.54, what would be the value of the resulting sample variance? Answered by Harley Weston. 





The mean and variance 
20080605 

From Donny: An investment will be worth $1,000, $2,000, or $5,000 at the end of the
year. The probabilities of these values are .25, .60, and .15, respectively.
Determine the mean and variance of the worth of the investment. Answered by Harley Weston. 





Expected value and standard deviation 
20080319 

From Patrick: Heres a question i cant figure out:
a small airline company has only three flights per day. The number of
delayed flights per day is regarded as a random variable, and I'm
supposed to calculate the expected
value and standard deviation of the number of delays.
the probability distribution looks like:
No. of Delays: 0 1 2 3
Prob. of delay: 05. 0.3 .1 .1 Answered by Harley Weston. 





Grouped data 
20071008 

From Nimra: The following sets of data represent the distributions of
house prices in the northeast and southwest of a country.
Random samples of 100 houses were selected in each region.
(a) Calculate the mean, median and standard deviation for Answered by Harley Weston. 





Sample variance and population variance 
20070922 

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. 





A statistics example 
20070802 

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. 





Types of variances 
20070508 

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 
20070428 

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. 





A one pass calculation of standard deviation 
20070319 

From Murtaza: Hi
I searched the listings but couldn't find what i am looking for. I have a dataset and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this : Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ??
Thanks in advance
Murtaza Answered by Penny Nom. 





Sample variance 
20050817 

From Rosalie: To give an unbiased estimate of the population variance, the denominator of the sample variance should be (n1) instead of n. I tried to convince myself by comparing the population variance and sample variance (with denominator n and n1): Answered by Penny Nom. 





Standard deviation 
20050102 

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. 





Incremental variance 
20040923 

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 quarterhour 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. 





E(X + Y) and V(X + Y) 
20030710 

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(xmean)^{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. 





Incremental standard deviation 
20030412 

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. 





Variance 
20021029 

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. 





Range of values for standard deviation 
20020322 

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. 





Can the standard deviation ever = 0? 
20020216 

From Karen: If given a class of 30 people who take a test with a mean of 80. Can the standard deviation ever = 0? If so, why? Answered by Penny Nom. 





Sample variance 
20000416 

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 n1 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. 





Standard Deviation 
19990711 

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. 





Mean and Standard Deviation 
19980422 

From Kit: i have a problem of maths. i think the level of the question is secondary. question: Find the mean and the standard deviation of the numbers:1, 3, 4, 5, 7. i hope u solve this question. thank you so much! Answered by Harley Weston. 





What is the variance of the difference of two binomials? 
19960208 

From Chris Johnson: My coworkers and I have come up with different estimates of the zstatistic, 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. 

