# Mean Absolute Deviation

In this worksheet, students must calculate the mean absolute deviation of a set of data.

Key stage:  KS 4

Curriculum topic:  Statistics

Difficulty level:

### QUESTION 1 of 10

Mean absolute deviation is a measure of how a set of numbers varies.

To calculate the mean absolute deviation, we work out the average of the absolute differences from the mean as follows:

Step 1

Work out the mean.

Step 2

For each number, subtract the mean and write down its absolute (positive size).

Step 3

Work out the mean of these absolute values.

Example

Over the course of five days, there were the following number of empty seats at a theatre.

 14 seats 18 seats 12 seats 20 seats 21 seats

Calculate the mean absolute deviation in the number of empty seats.

Step 1

Mean = (14 + 18 + 12 + 20 + 21) ÷ 5 = 85 ÷ 5 = 17

Step 2

|14 - 17| = |-3| = 3

|18 - 17| = |1| = 1

|12 - 17| = |-5| = 5

|20 - 17| = |3| = 3

|21 - 17| = |4| = 4

Step 3

Mean of 3, 1, 5, 3 and 4 = (3 + 1 + 5 + 3 + 4) ÷ 5 = 16 ÷ 5 = 3.2

Mean absolute deviation = 3.2

Over the course of five days, there were the following number of empty seats at a theatre.

 12 seats 14 seats 10 seats 20 seats 24 seats

Calculate the mean absolute deviation in the number of empty seats.

Just write the number.

Calculate the mean absolute deviation of the following set of numbers.

 12 5 3 8

Calculate the mean absolute deviation of the following set of numbers.

 12 7 1 8

Over the course of four days, the following number of people came into a cafe.

 82 95 67 112

Calculate the mean absolute deviation in the number of people.

Just write the number.

Over the course of a week, the following amounts of daily rainfall were recorded by Andrew.

 18 mm 20 mm 0 mm 11 mm 0 mm 5 mm 23 mm

Calculate the mean absolute deviation in the daily rainfall over the week.

Just write the number.

Janet measured the heights of 4 tomato seedlings in her greenhouse. The results in mm were:

 14 mm 25 mm 17 mm 20 mm

Calculate the mean absolute deviation in their heights.

Just write the number.

Calculate the mean absolute deviation of the following set of numbers to 1 decimal place.

 11 10 0 12 -3 5 7

Over the course of five days, Tom recorded the time it took him to cycle to school.

 12 mins 14 mins 11 mins 11 mins 12 mins

Calculate the mean absolute deviation in these times.

Just write the number.

Sumi counted the number of beans in four bags.

Her results were as follows:

 225 237 220 228

Calculate the mean absolute deviation in these numbers.

Just write the number.

Bill weighed five kilogram bags of flour and recorded their masses as follows:

 1022 g 1016 g 1008 g 1020 g 1021 g

Calculate the mean absolute deviation in these masses to 1 decimal place.

Just write the number.

• Question 1

Over the course of five days, there were the following number of empty seats at a theatre.

 12 seats 14 seats 10 seats 20 seats 24 seats

Calculate the mean absolute deviation in the number of empty seats.

Just write the number.

4.8
EDDIE SAYS

Step 1

Mean = (12 + 14 + 10 + 20 + 24) ÷ 5 = 80 ÷ 5 = 16

Step 2

|12 - 16| = |-4| = 4

|14 - 16| = |-2| = 2

|10 - 16| = |-6| = 6

|20 - 16| = |4| = 4

|24 - 16| = |8| = 8

Step 3

Mean of 4, 2, 6, 4 and 8 = (4 + 2 + 6 + 4 + 8) ÷ 5 = 24 ÷ 5 = 4.8

Mean absolute deviation = 4.8
• Question 2

Calculate the mean absolute deviation of the following set of numbers.

 12 5 3 8
3
EDDIE SAYS

Step 1

Mean = (12 + 5 + 3 + 8) ÷ 4 = 28 ÷ 4 = 7

Step 2

|12 - 7| = |5| = 5

|5 - 7| = |-2| = 2

|3 - 7| = |-4| = 4

|8 - 7| = |1| = 1

Step 3

Mean of 5, 2, 4, 1 = (5 + 2 + 4 + 1) ÷ 4 = 12 ÷ 4 = 3

Mean absolute deviation = 3
• Question 3

Calculate the mean absolute deviation of the following set of numbers.

 12 7 1 8
3
EDDIE SAYS

Step 1

Mean = (12 + 7 + 1 + 8) ÷ 4 = 28 ÷ 4 = 7

Step 2

|12 - 7| = |5| = 5

|7 - 7| = |0| = 0

|1 - 7| = |-6| = 6

|8 - 7| = |1| = 1

Step 3

Mean of 5, 0, 6, 1 = (5 + 0 + 6 + 1) ÷ 4 = 12 ÷ 4 = 3

Mean absolute deviation = 3
• Question 4

Over the course of four days, the following number of people came into a cafe.

 82 95 67 112

Calculate the mean absolute deviation in the number of people.

Just write the number.

14.5
EDDIE SAYS

Step 1

Mean = (82 + 95 + 67 + 112) ÷ 4 = 356 ÷ 4 = 89

Step 2

|82 - 89| = |-7| = 7

|95 - 89| = |6| = 6

|67 - 89| = |-22| = 22

|112 - 89| = |23| = 23

Step 3

Mean of 7, 6, 22, 23 = (7 + 6 + 22 + 23) ÷ 4 = 58 ÷ 4 = 14.5

Mean absolute deviation = 14.5
• Question 5

Over the course of a week, the following amounts of daily rainfall were recorded by Andrew.

 18 mm 20 mm 0 mm 11 mm 0 mm 5 mm 23 mm

Calculate the mean absolute deviation in the daily rainfall over the week.

Just write the number.

8
EDDIE SAYS

Step 1

Mean = (18 + 20 + 0 + 11 + 0 + 5 + 23) ÷ 7 = 77 ÷ 7 = 11

Step 2

|18 - 11| = |7| = 7

|20 - 11| = |9| = 9

|0 - 11| = |-11| = 11

|11 - 11| = |0| = 0

|0 - 11| = |-11| = 11

|5 - 11| = |-6| = 6

|23 - 11| = |12| = 12

Step 3

Mean of 7, 9, 11, 0, 11, 6, 12 = (7 + 9 + 11 + 0 + 11 + 6 + 12) ÷ 7 = 56 ÷ 7 = 8

Mean absolute deviation = 8
• Question 6

Janet measured the heights of 4 tomato seedlings in her greenhouse. The results in mm were:

 14 mm 25 mm 17 mm 20 mm

Calculate the mean absolute deviation in their heights.

Just write the number.

3.5
EDDIE SAYS

Step 1

Mean = (14 + 25 + 17 + 20) ÷ 4 = 76 ÷ 4 = 19

Step 2

|14 - 19| = |-5| = 5

|25 - 19| = |6| = 6

|17 - 19| = |-2| = 2

|20 - 19| = |1| = 1

Step 3

Mean of 5, 6, 2, 1 = (5 + 6 + 2 + 1) ÷ 4 = 14 ÷ 4 = 3.5

Mean absolute deviation = 3.5
• Question 7

Calculate the mean absolute deviation of the following set of numbers to 1 decimal place.

 11 10 0 12 -3 5 7
4.6
EDDIE SAYS

Step 1

Mean = (11 + 10 + 0 + 12 + -3 + 5 + 7) ÷ 7 = 42 ÷ 7 = 6

Step 2

|11 - 6| = |5| = 5

|10 - 6| = |4| = 4

|0 - 6| = |-6| = 6

|12 - 6| = |6| = 6

|-3 - 6| = |-9| = 9

|5 - 6| = |-1| = 1

|7 - 6| = |1| = 1

Step 3

Mean of 5, 4, 6, 6, 9, 1, 1 = (5 + 4 + 6 + 6 + 9 + 1 + 1) ÷ 7 = 32 ÷ 7 = 4.5714...

Mean absolute deviation = 4.6
• Question 8

Over the course of five days, Tom recorded the time it took him to cycle to school.

 12 mins 14 mins 11 mins 11 mins 12 mins

Calculate the mean absolute deviation in these times.

Just write the number.

0.8
EDDIE SAYS

Step 1

Mean = (12 + 14 + 11 + 11 + 12) ÷ 5 = 60 ÷ 5 = 12

Step 2

|12 - 12| = |0| = 0

|14 - 12| = |2| = 2

|11 - 12| = |-1| = 1

|11 - 12| = |-1| = 1

|12 - 12| = |0| = 0

Step 3

Mean of 0, 2, 1, 1 and 0 = (0 + 2 + 1 + 1 + 0) ÷ 5 = 4 ÷ 5 = 0.8

Mean absolute deviation = 0.8
• Question 9

Sumi counted the number of beans in four bags.

Her results were as follows:

 225 237 220 228

Calculate the mean absolute deviation in these numbers.

Just write the number.

5
EDDIE SAYS

Step 1

Mean = (225 + 237 + 220 + 228) ÷ 4 = 910 ÷ 4 = 227.5

Step 2

|225 - 227.5| = |-2.5| = 2.5

|237 - 227.5| = |9.5| = 9.5

|220 - 227.5| = |-7.5| = 7.5

|228 - 227.5| = |0.5| = 0.5

Step 3

Mean of 2.5, 9.5, 7.5, 0.5 = (2.5 + 9.5 + 7.5 + 0.5) ÷ 4 = 20 ÷ 4 = 5

Mean absolute deviation = 5
• Question 10

Bill weighed five kilogram bags of flour and recorded their masses as follows:

 1022 g 1016 g 1008 g 1020 g 1021 g

Calculate the mean absolute deviation in these masses to 1 decimal place.

Just write the number.

4.3
EDDIE SAYS

Step 1

Mean = (1022 + 1016 + 1008 + 1020 + 1021) ÷ 5 = 5087 ÷ 5 = 1017.4

Step 2

|1022 - 1017.4| = |4.6| = 4.6

|1016 - 1017.4| = |-1.4| = 1.4

|1008 - 1017.4| = |-9.4| = 9.4

|1020 - 1017.4| = |2.6| = 2.6

|1021 - 1017.4| = |3.6| = 3.6

Step 3

Mean of 4.6, 1.4, 9.4, 2.6, 3.6 = (4.6 + 1.4 + 9.4 + 2.6 + 3.6) ÷ 5 = 21.6 ÷ 5 = 4.32

Mean absolute deviation = 4.3
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