Mean, Median and Mode Practice Tutorial and Practice Questions

Median, Mode and Mean questions appear on standardized tests in most High School, College and some Nursing Entrance Tests

Mean, Median and Mode

Mean, mode and median are basic statistical tools used to calculate different types of averages. Below is a quick tutorial followed by practice questions.

Mean
Mean is the most common form of average used. To calculate mean, you simple add up all the values of data given and divide by the number data provided.

Example
Find the mean of 8, 5, 7, 10, 15, 21
Sum of values = 8 + 5 + 7 + 10 + 15 + 21 = 66
Number of data = 6
Mean = 66/6 = 11

Median
Median refers to the middle value among a set or series of values after they have been arranged in numerical order. Median thus means the middle of the set of values. When two numbers fall in the middle, you simple add the value of the two numbers and divide by 2 to get the middle of the two numbers.

Example
Arrange these numbers in ascending order and then find the median
First arrange in ascending order 8, 5, 7, 10, 15, 21
= 5, 7, 8, 10, 15, 21

There are 6 numbers on the series and two fall in the middle = 8 and 10
The median = 8 + 10/2  = 18/2 =9

Mode
Mode refers to the most occurring number or value among a set of values. Note that it is possible not to have a most occurring number and then the answer becomes ‘No Mode’

Example
8, 5, 7, 10, 15, 21, 5, 7, 2, 5
Mode refers to the most occurring number 8, 10, 15, 2 and 21 occur once

5 occurs 3 times
7 occurs 2 times
The most occurring number is 5, which occurs three times.

1. Find the median of the set of numbers: 1,2,3,4,5,6,7,8,9 and 10.

a. 55
b. 10
c. 1
d. 5.5

2. Find the median of the set of numbers:  21, 3, 7, 17, 19, 31, 46, 20 and 43.

a. 19
b. 20
c. 3
d. 167

3. Find the median of the set of numbers:  100, 200, 450, 29, 1029, 300 and 2001.

a. 300
b. 29
c. 7
d. 4,080

4. The following represents age distribution of students in an elementary class. Find the mode of the values: 7, 9, 10, 13, 11, 7, 9, 19, 12, 11, 9, 7, 9, 10, 11.

a. 7
b. 9
c. 10
d. 11

5. Find the mode from these test results: 90, 80, 77, 86, 90, 91, 77, 66, 69, 65, 43, 65, 75, 43, 90.

a. 43
b. 77
c. 65
d. 90

6. Find the mode from these test results: 17, 19, 18, 17, 18, 19, 11, 17, 16, 19, 15, 15, 15, 17, 13, 11.

a. 15
b. 11
c. 17
d. 19

7. Find the mean of these set of numbers: 100, 1050, 320, 600 and 150.

a. 333
b. 444
c. 440
d. 320

8. The following numbers represent the ages of people on a bus: 3, 6, 27, 13, 6, 8, 12, 20, 5, 10. Calculate their mean of their ages.

a. 11
b. 6
c. 9
d. 110

9. These numbers are taken from the number of people that attended a particular church every Friday for 7 weeks: 62, 18, 39, 13, 16, 37, 25. Find the mean.

a. 25
b. 210
c. 62
d. 30

1. D
First arrange the numbers in a numerical sequence: 1,2,3,4,5,6,7,8,9, 10. Then find the middle number or numbers. The middle numbers are 5 and 6. The median = 5 + 6/2 = 11/2 = 5.5

2. B
First arrange the numbers in a numerical sequence: 3,7, 17, 19, 20, 21, 31, 43, 46. Next find the middle number. The median = 20

3. A
First arrange the numbers in a numerical sequence: 29,100, 200, 300, 450, 1029, 2001. Next find the middle number. The median = 300

4. B
Simply find the most recurring number. The most occurring number in the series is 9

5. D
Simply find the most recurring number. The most occurring number in the series is 90.

6. C
Simply find the most recurring number. The most occurring number in the series is 17.

7. B
First add all the numbers 100 + 1050 + 320 + 600 + 150 = 2220. Then divide by 5 (the number of data provided) = 2220/5 = 444

8. A
First add all the numbers 3 + 6 + 27 + 13 + 6 + 8 + 12 + 20 + 5 + 10 = 110. Then divide by 10 (the number of data provided) = 110/10 = 11

9. D
First add all the numbers 62 + 18 + 39 + 13 + 16 + 37 + 25 = 210. Then divide by 7 (the number of data provided) = 210/7 = 30