Answered

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?

A2.2

B5

C22

D50

Verified Answer :

The absolute deviation for this problem is 2.2.

Answer:

Option A - 2.2

Step-by-step 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.

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

\(Mean = \frac{1+2+ 2+ 4+ 5+ 6+ 6+ 8+ 8+ 8}{10}\)

\(Mean = \frac{50}{10}\)

\(Mean = 5\)

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.

\(\Rightarrow\frac{22}{10}=2.2\)

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

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