## The Mode, Mean and Median, are types of averages.

The mean is the average calculated by adding the numbers and dividing by the number of items in the data set. The median is the middle value in a data set. To calculate the median, put the numbers in order, and the median will be the middle number. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

See our example below. The mode is the most frequently occurring number. If no number is repeated, then there is no mode.

**Examples**

Find the median, mode and mean of the following list:

6, 7, 8, 12, 14, 6, 7, 10

**Find the mean**

First add the numbers

6 + 7 + 8 + 12 + 14 + 6 + 7 + 10 = 70

There are 8 numbers in the list, so divide by 9

70/8 = 8.75 = mean

**Find the median**

First put the numbers in order

6, 6, 7, 7, 8, 10, 12, 14,

The data set has an even number of numbers, so the median is the average of 7 and 8. (7 + 8)/2 = 7.5

**Find the mode**

The mode is the most frequently occurring number. Here

6 and 7 both occur twice, so they are both considered the

mode.

**1. Find the mean of these set of numbers – 200,000, 10,020, 30,000, 15,000 1080**

a. 1080

b. 15,000

c. 256,100

d. 51,220

**2. Find the mean of these set of numbers – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10**

a. 55

b. 5.5

c. 11

d. 10

**3. Find the mean of these set of numbers – 2.5, 10.2, 4.5, 1.25, 7.05, 20.8**

a. 7.6

b. 45.6

c. 7

d. 1.25

## Median Questions

**4. Find the median of the set of numbers – 3, 1, 9, 7, 13, 11, 15, 21, 15, 9, 7**

a. 11

b. 1

c. 9

d. 90

**5. Find the median of these set of test scores taken from a class of students – 90, 80, 77, 86, 50, 91, 73, 66, 69, 45, 43, 65, 75**

a. 13

b. 73

c. 9

d. 706

**6. Find the median of 32, 64, 109, 67 and 3**

a. 64

b. 3

c. 275

d. 5

## Mode Questions

**7. Find the mode from these numbers – 7,2,3,9,6,5,1,4,8**

a. 1

b. 5

c. 9

d. None of the above

**8. Find the mode from these numbers – 190, 280, 177, 186, 180, 291, 177, 166, 169, 165, 243, 165, 177, 243, 190**

a. 190

b. 177

c. 165

d. 243

**9. Find the mode from these test results – 2, 4, 2, 6, 4, 9, 6, 7, 2, 9, 7, 6, 4, 10, 10, 2, 6, 7, 9**

a. 2 and 9

b. 2

c. 2 and 6

d. 2 and 7

## Answer Key

**1. D**

First add all the numbers 200,000 + 10,020 + 30,000 + 15,000 + 1080 = 256,100. Then divide by 5 (the number of data provided) = 256,100/5 = 51,220

**2. C**

First add all the numbers 1 + 2 + 3 + 4 + 5 +6 + 7 +8 + 9 + 10 = 55. Then divide by 10 (the number of data provided) = 55/5 = 11

**3. A**

First add all the numbers 2.5 + 9.5 + 4.5 + 1.25 + 7.05 + 20.8 = 45.6. Then divide by 6 (the number of data provided) = 45.6/6 = 7.6

**4. C**

First arrange the numbers in a numerical sequence – 1, 3, 7, 7, 9, 9, 11, 13, 15, 15, 21. Next find the middle number. The median = 9

**5. B**

First arrange the numbers in a numerical sequence – 43, 45, 50, 65, 66, 69, 73, 75, 77, 80, 86, 90, 91. Next find the middle number. The median = 73

**6. A**

First arrange the numbers in a numerical sequence – 3, 32, 64, 67, 109. Next find the middle number. The median = 64

**7. D**

Simply find the most recurring number. All the numbers in the series appeared only once. The answer is No Mode

**8. D**

Simply find the most recurring number. The most occurring number in the series is 177

**9. C**

Simply find the most recurring number. The most occurring numbers in the series is 2 and 6

Written by:

**Modified: ** [insert_php] the_modified_date(‘F jS, Y’); [/insert_php] [insert_php] the_modified_date(‘F jS, Y’); [/insert_php]

**Published: ** [insert_php] the_time(‘F jS, Y’); [/insert_php]