Question

Use the data set to answer the question. {22,26,28,35,45,63,91} What is the mean absolute deviation (MAD) of the data set? Enter your answer as a number rounded to the nearest tenth

Answer 1

mean absolute deviation is 18.85

Explanation:

Step 1:-

Given observation values 22,26,28,35,45,63,91

`mean (x ) = (22+26+28+35+45+63+91)/(7)`

mean = 44.28≅ 44

Step2:-

The deviations of the respective observations from the mean (x)

That is
`x_(i)-x`

22-44, 26-44,28-44,35-44,45-44,63-44,91-44

-22, -18 ,-16 ,-9, 1, 19, 47

Step 3:-

The absolute values of the given data

`x_(i)-x`

modulus of all these values

22,18,16,9.1,19,47

Step 4:-

Mean absolute deviation M.D=∑
`(x_(i) - x )/(n)`

`MAD = (22+18+16+9+1+19+47)/(7)`

on simplification we get mean absolute deviation is 18.85