







How many students passed the test? 
20180720 

From florian: In Mr. Edgecomb's math class, 30 students took an exam on statistics. If the average passing grade was 84, the average failing grade was 60, and the overall average was 80, how many students passed the test? Answered by Penny Nom. 





How many pet dogs? 
20170926 

From Michelle: In 2016 there were about 135 million households in the United States. 36.5% of the households own at least one dog. On average, these households have 1.6 dogs. How many millins of pet dogs were in the United States in 2016? Answered by Penny Nom. 





Average price 
20170915 

From Annette: If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price Answered by Penny Nom. 





The average rate of change of cot(t) 
20170118 

From Brianna: Hello!
It's been a while since I've taken a math course, and I'm stuck on a problem in my calculus course.
The question is this:
Find the average rate of change of the function over the given interval.
h(t)=cot(t) a) [5pi/4, 7pi/4] Answered by Penny Nom. 





How can he raise his average to 90? 
20151229 

From Raj: Harris has an 87 in a class where daily works count 20%, quizzes count 20% and tests count 60%.
If there are only two test scores what must the score on his second test to raise his average to 90? Answered by Penny Nom. 





Average rate for a return trip 
20150314 

From Michael: Jeffrey drove to a town 25 miles away at an average speed of 50 miles per hour. The return trip along the same route took 20 minutes longer than the trip to town. Determine the average speed in miles per hour for Jeffrey's round trip. Answered by Penny Nom. 





A train from Vancouver to Whistler 
20150202 

From Tea: Serena and Nina are taking a train from Vancouver to Whistler, a 160km trip. If the average speed is decreased by 16km/hr, the trip will be 1/2 hours longer. What is the average speed of the train?
Thanks :) Answered by Penny Nom. 





The average of 9 numbers is 45 
20140912 

From rizza: The average of 9 numbers is 45. If 90 and 88 are added to the set of numbers. What will be the resulting average? Answered by Penny Nom. 





The average age of a group of 10 students 
20140911 

From sujan: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group . What is the average age of the two new students who joined the group? Answered by Robert Dawson and Penny Nom. 





What is the average of first 100 even numbers? 
20140802 

From Faizan: What is the average of first 100 even numbers? Answered by Chris Fisher. 





A word problem concerning averages 
20140726 

From Bernie: The average weight of a team of children is 50kg, Todd who weighs 56 kg then joins the team. The average weight of the new team is 51. How many children in the original team? Answered by Penny Nom. 





Adding speeds 
20120826 

From Roy: May I ask if it is correct to add the following with units included? Some tell me that the units cannot be included in the addition because we cannot add speed. Answered by Harley Weston. 





What was the class average? 
20120420 

From olwale: a class which consist of 15 boys and 10 girls sit for a test. the average score of the boys is 20 and the girls' is 25. find the average score of the class. Answered by Penny Nom. 





Mean and Average 
20120103 

From john: what is the difference between average and mean Answered by Robert Dawson. 





The average age of 300 cars 
20111122 

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 
Thanks Answered by Penny Nom. 





The average speed for the whole journey 
20111030 

From Shahzad: a train travels 68 Km at an average speed of 51Km/h. It then travels another 20Km at an average speed of 40Km/h before reaching its destination. Calculate the average speed for the whole journey? Answered by Penny Nom. 





Find his income on the fourth week of August. 
20110322 

From Abeth: The average weekly income of MJ for the first three weeks of August was 3,600 and his average weekly income for four weeks is 3950. Find his income on the fourth week of August. Answered by Penny Nom. 





Average speed 
20110307 

From West: Calculate the distance (in km) that Larry runs if he maintains an average speed of 8km/hr for 45 minutes Answered by Penny Nom. 





The average over two semesters 
20100120 

From edy: 6 courses have an average of 100 in the first semester
5courses have an average of 90 in the second semester
what is the average of the two semester , method of calculation , how come to have 95.4545 Answered by Penny Nom. 





Average speed 
20090911 

From john: Sally travels by car from one city to another. She drives for 20.0 min at 68.0 km/h, 40.0 min at 37.0 km/h, and 51.0 min at 77.0 km/h, and she spends 12.0 min eating lunch and buying gas.
What is the average speed for the trip? Answered by Penny Nom. 





Average speed 
20090820 

From Christina: We ran 3.4 miles in 40 minutes. What was our average speed? Answered by Leeanne Boehm. 





Averaging percentages 
20090614 

From Alan: Can you add percentages and then divide them by the number of percentages to get the average percentage.
I.E day 1 100% day 2 100% day 3 95% average= 98.3%
is the above possible or is it not done, I have a dispute with a work colleague over this.
many thanks Answered by Harley Weston. 





Driving to school and back 
20090517 

From marylyne: suppose you are late for school and you drive from your house at a constant rate of 70 mph.when class is over, you drive home at a more leisurely 50mph. what is your average speed? Answered by Penny Nom. 





Mean 
20090502 

From debra: a hot dog sales per week monday, 100 = tuesday,87 = wednesday, 95 = thursday, 125 = friday, 210 = saturday, 250 = sunday, 57 = what is the mean sales per day? Answered by Penny Nom. 





Interest rate over two periods 
20090412 

From Kenneth: Hello:
How is the average determined for the following amount if it earns
compound interest?
Here are my calculations, but I'm not certain that they are correct:
Initial amount invested $500.00:
$500.00 @ 5% = $525.00.
$525.00 @ 2% = $514.50.
$14.50/$500.00 = 2.9% divided by 2 equals an average of 1.45%.
If this average, 1.45%, is correct, how can I use 5% and 2% to
determine the same average?
Is it possible?
I thank you for your reply. Answered by Penny Nom. 





A trip at two different speeds 
20090328 

From A student: Good afternoon!
An automobile travels 4 hours at an average speed of 42MPH. How much
longer must the truck travel at an average speed of 55MPH so the
average speed for the total trip will be 50MPH?
Thank you for your assistance! Answered by Penny Nom. 





Whitney's average test score was 79 
20090130 

From dawn: After 5 tests, Whitney's average test score was 79. After she scored 85 on the 6th test. What was her new average? Answered by Penny Nom. 





Average and total 
20090110 

From cecil: the average of six number is 84. what is the total Answered by Stephen La Rocque and Penny Nom. 





A weighted average 
20081127 

From Kenneth: I am interested in determining the answers to the following question by using some type of weighted average:
An investor has $30,000 to invest at simple interest in two accounts. One account earns 2% and the second earns 5%. How much must he invest in each account if his total return is 4% or $1,200? Answered by Penny. 





The average height of an attic 
20080912 

From oliver: I need to find out the average height of a specific volume/area.
a standard house shape side walls height 10m, height in centre of house 15m.
width 15m length 25m (the roof spans the width)
Within the house in the corner there is a (box shape) room which is 5m in height by 3m wide and 4 m long
How do i work out the average height of the space directly above the room (same floor area)? Answered by Stephen La Rocque and Harley Weston. 





What will be the resulting average? 
20080905 

From jean: the average of 9 is 54.if 84 and 90 are added to the set of numbers ,what will be the resulting average? Answered by Penny Nom. 





The average rate of change 
20080329 

From Tom: For the function x/3x1 find the average rate of change between the interval x=1 and x=5? Answered by Harley Weston. 





Average and mean 
20080317 

From A student: Mean and average are the same propeties of the set of elements, if there is average then why mathematician need the mean ? Answered by Penny Nom. 





Average speed up and down a hill 
20080309 

From Judith: An old brokendown ar has to travel a two miles route, up and down a hill.
Because it is so old, the car travels the first mile  the ascent  at an average
speed of fifteen miles per hour. How fast must it cover the second mile 
the decent  to achieve an average speed of thirty miles per hours?
(There is a missing variable, but what is it?) Answered by Penny Nom. 





Stacks of blocks 
20080207 

From Tammy: i need help for my son he is given 3 stacks of cubes. the 1rst stack has 3 the 2nd stack has 2 the 3rd stack has 4
the question is draw the stacks of cubes so they are arranged correctly to find the mean. what is the mean of the data? Answered by Stephen La Rocque and Penny Nom. 





How old is the 11th person? 
20071208 

From Jamie: Ten people are in a room, and their mean age is 15. After another person enters the room, the mean age is now 18. How old is the person that walked in? Answered by Jesse McLeod and Stephen La Rocque. 





Six crates of cantaloupes 
20071105 

From BARBARA: The average weight 6 crates of cantaloupes is 61 lbs, if 3 of the crates weigh 72, 59, and 70 lbs. which of the following could be the weight in pounds of the other 3 crates?
a. 49,59,60
b. 51,53,54
c. 53,57,58
d. 54,56,60
e. 57,57,57 Answered by Stephen La Rocque and Penny Nom. 





The aggregate percentage for the year 
20071011 

From Lisa: I would like to add up twelve percentages then divide it by 12 to get the aggregate percentage for the year. How do I accomplish this task? Thanks. Answered by Penny Nom. 





The average rate of change of a function 
20071011 

From vern: Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]? Answered by Harley Weston. 





calculating percentages for my class 
20071009 

From Cori: I teach a class in which there are seven projects/quizzes worth 10% each,
and the midterm and the final are each worth 15%. No problem figuring out
their final grade, but I have to give a midterm average, having only FOUR
of the seven 10% things, and the midterm test. The closest I've come to
an accurate "average" is to just add them together (as equals) and average them. Answered by Victoria West & Harley Weston. 





The change in an average 
20070819 

From farah: the average height of a group of 25 students goes up by 2 cm when astudent of height 165 cm replaces a student from the group.what is the height of the boy who went out of the group? Answered by Stephen La Rocque. 





What was the average? 
20070808 

From Leroy: A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test? Answered by Penny Nom. 





Average annual earnings per share 
20070807 

From Arul: A corporation with 5,000,000 shares of publicly listed stock reported total earnings of $7.20 per share for the first 9 months of operation. During the final quarter the number of publicly listed shares was increased to 10,000,000 shares, and fourth quarter earnings were reported as $1.25 per share. What are the average annual earnings per share based on the number of shares at the end of the year? Answered by Stephen La Rocque. 





Average speeds 
20070622 

From Dee: A guy goes 3.1m a second for 29 seconds in a golf cart. He then walks 1.5 meters a second. How long does he have to walk to get the average speed of 2.1m a second? Answered by Stephen La Rocque. 





The "mode" of a set of numbers 
20070606 

From Anthony's mom: we have a graph: Kindergarten has 1, 1st has 5, 2nd has 4, 3rd has 3
is the mode "1st grade" because there are more children in that grade? Answered by Stephen La Rocque. 





How to increase your average 
20070524 

From Janna: after taking 4 quizes your average is 71 out of 100. what must your average
on the next 5 quizes be to increase your average to an 81 out of 100? Answered by Penny Nom. 





Average 
20070506 

From michelle: the average of x and y is 20. If z = 5, what is the average of x, y, and z. Answered by Stephen La Rocque. 





An average homework grade 
20070426 

From vince: If your homework grades is only 15% of the total grades and with an average
homework grade of 90% what is your earn point for the homework
earn point = average times percent Answered by Stephen La Rocque. 





Producing chocolate bars 
20070426 

From anne: If you have to produce an average of 114 bars of chocolate over 7.5 hours how many do you have to produce over 9.5 hours. Answered by Penny Nom. 





Approximate average speeds 
20070319 

From Anne: A bicyclist pedaled up a 2 mile long hill averaging 4 miles per hour. Upon reaching the top, the bicyclist headed down a 6 mile descent averaging 26 mph. What was the bicyclist's approximate average speed?
Thanks very much in advance!! Answered by Stephen La Rocque and Penny Nom. 





The average of 3 tests 
20061212 

From Charles: If you average 84 on first three test and the first score was 67. The second score was 7 less than the third score. What was the score on the second and third test. Answered by Stephen La Rocque. 





Quiz grades 
20061205 

From Patricia: Your quiz grades are 73, 75, 89 and 91. What is the lowest grade you can obtain on the last quiz and still achieve an average at least 85? Answered by Stephen La Rocque and Penny Nom. 





Power walking 
20060730 

From Wendy: I have an exercise routine of 'power walking', approx. 56 days per week. I carry a pedometer with me during these walks so that I can keep track of the distance of each walk. I've created a weekly walking chart on my computer, so each time I get back from a walk, I enter my stats, such as kilometers and miles walked that day, as well as my start and finish time. At the end of each week, before I printed out my completed chart, I would calculate out what my average walking distance was, for that particular week.
At the end of each month, I would calculate:
[1] I'd add up my total kilometers and miles walked for that month. (a no brainer ~ I could do that one!)
**But also, I would work out the percentages of the following:
[A] What my average daily distance p/walk was, for that month
[B] What my average time spent, per walk was, for that month Answered by Penny Nom. 





The average of a function 
20060411 

From Justin: Find the average value of the following function from x=0 to x=7
f(x)=3x+4 Answered by Penny Nom. 





The average of monthly averages 
20060406 

From Ray: I have the averages of some data in percentages. the data is rather large, how can i find the average of these averages without going back to the original data? Is there a Factor or Constant that i could multiply or devide or add and get the average of these averages without resorting to the raw data. Answered by Steve La Rocque and Harley Weston. 





Divide the product of three consecutive positive integers by their mean 
20060312 

From Sandy: When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers? Answered by Stephen La Rocque. 





The average of 4 numbers is 5. 
20060102 

From Sheri: The average of 4 numbers is 5. I have 3 of the numbers already 5,8,4,? How do i find out what the last number to give me the average of 5? Answered by Penny Nom. 





Mean and average 
20051222 

From Jerry: This is just a question from a degreed engineer that has a "understanding" problem. please go to http://www.metrika.com/3medical/hemoglobinm.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. 





Mathilda and Matthew 
20051218 

From A student:
Question: 1) The average of 12 is 5. The average of of 8 of these numbers ia 6. What is the average of the other four.
2)Mathilda is playing a mathematical game with Matthew. Each player starts from a point, then moves in a straight line to a second point,then to a third and so on. The moves are not made randomly, but are determined by a mathematical rule. The object of the game is to find the rule. It is Mathilda's turn to move on the grid . She starts at point M (3,9), moves to point N (2,4) and then to point O (0,0). Given Mathilda's rule, what could be the coordinates of the next point to which she might move?
Answered by Penny Nom. 





Half way between 
20040908 

From Ben: Find the number halfway between the number shown
751,843 Answered by Penny Nom. 





X bar 
20031104 

From mary: Remind me what this means:
_
X
Answered by Andrei Volodin. 





Means 
20031028 

From Abdu:
Question: 80,80,84,85,88,92,97,98 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. 





Averages of Averages 
20021221 

From Amy: If in the month of October the % of Payments Received was 80.74% and in November it decreased to 69.36%. Can you take the 80.7469.36/69.36 to get the % of difference. In otherwords can you take the % of difference when the numbers you are comparing are %'s???? Can you also take an average of an average? For example, average number of payments received in October was 25.00%, average number of payments received November was 50.00%, and the average number of payments received in December was 15.00%. Do you average (25.00%, 50.00% and 15.00%) or do you have to go back to the numbers that calculated the averages. For example, October 25.00% was based on 25 payments being received out of a possible 100. So instead of taking the average of the averages, do you take the average payments and the average customers over the 3 months and calculate the average??? Answered by Harley Weston. 





Averaging grades 
20021024 

From Richard: I'm using a grading program for the first time this year. (ok, that's not a question) I require my students to record their grades in a Scorekeeper when they get them back. I'd like to know if my students can keep up with averaging their grades just as the grading programs automatically averages them when I put them in the spreadsheet. Answered by Penny Nom and Claude Tardif. 





The mean distance travelled 
20020607 

From A student: If Rosalia travels 1000 km Sheree travels 280 km Daniel travels 50 km Mica travels 200 km Connor travels 500 km Eric travels 250 km Hillary travels 300 km What was the mean distance travelled? How do you arrive at the answer? Answered by Penny Nom. 





The average of two averages 
20020522 

From RJ: in a class with 22 students, the average garde on an exam was 68%, in another class with 32 students, the average grade on the same exam was 78%, what was the overall for the two classes? round your answers to the nearest whole number. Answered by Leeanne Boehm. 





Number conversions and averages 
20020203 

From A student: A table has the measurements of 1.6m by 2m, how much material is needed to cover table? I converted to cm then multiplied but got an answer of 32000cm ,so I divide by 100 to get to metres  the answer was 320 which I know is wrong  please explain!! Also I need to explain in my own words what an 'average' is and I am struggling. Answered by Penny Nom. 





The average of two polygons 
20011023 

From Irene: How can I prove that the average of two polygons will give me another one? Answered by Walter Whiteley. 





What did the girls score on average? 
20010720 

From Rajesh: The students of two schools were sitting the same test. The students attending the first school scored 74 on average; within this the average scores of the boys and the girls were 71 and 76, respectively. The corresponding scores in the other school were 84, 81 and 90, respectively. If the average score of all boys was 79, what did the girls score on average? Answered by Penny Nom. 





The average value of a continuous function 
20010508 

From Esther: The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Answered by Harley Weston. 





Average speed 
20010501 

From Tom: A ship goes in one direction, west to Hawaii, at 20 nautical miles per hour and, because of the wind, makes the return trip at 30 nautical miles per hour. What is the average speed? Answered by Claude Tardif. 





Lots of coins 
20010426 

From A student: I purchase 2 million coins at 9.75 I purchase 1 milion coins at 8 what is the formula to calculate my average cost? Answered by Penny Nom. 





A few problems 
20010422 

From Carol: Hello I am a College student trying get through my elmentry concepts class. I am also working with the middle and elementry school student with their work. I was given a few problems to work on and i am having a hard time explaining them to students. DO you think you can help with a coupld of these questions! Answered by Penny Nom. 





Cincinnati to WinstonSalem 
20010123 

From Belinda: Joan Bedney travels from Cincinnati to WinstonSalem at an average rate of 40 miles per hour and returns at an average rate of 60 miles per hour. What is her average speed for the trip? Answered by Leeanne Boehm and Claude Tardif. 





What is the difference between Mean and Average? 
20001213 

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 
20001102 

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. 





Mr. Edgecomb's math exam 
20000917 

From Rachel: In Mr. Edgecomb's math class, 30 students took an exam on statistics. If the average passing grade was 84, the average failing grade was 60, and the overall average was 80, how many students passed the test? 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. 





Word problems 
20000331 

From Amy: Question:  a north bound train left at noon. four hours later a south bound train left the same station. at 5 o'clook they were 160 miles apart. what was the rate of both if the north bound train was going 20 miles faster than the other one.
 clark's final exam was given 5 times the weight of the weight of a weekly test. the avgerage of 15 weekly test was 91. the overall weighted average was 85. what did he make on the final.
Answered by Penny Nom. 





Travelling from A to B 
20000320 

From Matt: A car is traveling from point A to point B. Point A and point B are 30 miles apart. A car travels 30 miles an hour from point A to point B and then goes back to point A. How fast does the car have to go back to average 60 miles an hour? Answered by Claude Tardif. 





.400 in Baseball 
19991215 

From Nieve Nielson: I have several questions to ask about the probability of getting a .400 in baseball:  What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?
 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:
 Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?
Answered by Chris Fisher. 





The sixth game 
19991116 

From Stephanie Sprunger: Janice scored 18,21,27,16,and 19 points in five basketball games. How many points must she score in the next game to raise her average to 22 points per game? Answered by Penny Nom. 





The average rate of change of a function 
19990420 

From Tammy: Suppose that the average rate of change of a function f over the interval from x=3 to x=3+h is given by 5e^h4cos(2h). what is f'(3)? I would appreciate any help with this question. Answered by Harley Weston. 





The halfway mark 
19990420 

From Sherry & Tom McGee: How do you figure the halfway mark between 1/3 and 2/3 as a fraction and a decimal point? Answered by Penny Nom. 





Prime dates 
19990325 

From Jessica Brown: I'm asking how do you figure out all the prime numbers in a year and, whats the average amount of prime numbers per week. Answered by Jack LeSage and Penny Nom. 





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. 

