Question

Cara collected data from 10 students about what their favorite number was between 1 and 10.

The students responses were: 1, 2, 2, 4, 5, 6, 6, 8, 8, 8

What is the absolute deviation?

A) 2.2

B) 5

C) 22

D) 50

Answer 1

The absolute deviation for this problem is 2.2.

Answer 2

Option A - 2.2

Explanation:

Given : Data of 10 students

The students responses were: 1, 2, 2, 4, 5, 6, 6, 8, 8, 8

To find : The absolute deviation

Solution :

Step 1: We calculate the mean.

`Mean = \frac{\text{Sum of the numbers}}{\text{Total numbers}}`

`Mean = (1+2+ 2+ 4+ 5+ 6+ 6+ 8+ 8+ 8)/(10)`

`Mean = (50)/(10)`

`Mean = 5`

Step 2: Then we calculate how far away each data point is from the mean using positive distances these are known as absolute deviations.

Data point Distance from mean

1 |5-1| =4

2 |5-2| =3

2 |5-2| =3

4 |5-4| =1

5 |5-5| =0

6 |5-6| =1

6 |5-6| =1

8 |5-8| =3

8 |5-8| =3

8 |5-8| =3

Step 3: Add the deviations together.

`\Rightarrow 4+3+3+1+0+1+1+3+3+3= 22`

Step 4: Finally Divide the sum by the number of data points to get mean of absolute deviation.

`\Rightarrow(22)/(10)=2.2`

Therefore,Option A is correct the mean absolute deviation is 2.2.