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, like this: 42.5

Answer 1

Answer:

$M.A.D = 18.9$

Step-by-step explanation:

Given: 22,26,28,35,45,63,91

Required: Mean Absolute Deviation

The first step is to solve for the mean of the given data

$Mean = \frac{\sum x}{n}$

where x->22,26,28,35,45,63,91 and n = 7

$Mean = \frac{22+26+28+35+45+63+91}{7}\\Mean = \frac{310}{7}\\Mean = 44.29$

Then; subtract the calculated mean from each data

$22 - 44.29 = -22.29\\26 - 44.29 = -18.29\\28 - 44.29 = -16.29\\35 - 44.29 = -9.29\\45 - 44.29 = 0.71\\63 - 44.29 = 18.71\\91 - 44.29 = 46.71$

Get Absolute Values of the above results

$|-22.29| = 22.29\\|-18.29| = 18.29 \\|-16.29| = 16.29\\|-9.29| = 9.29\\|0.71| = 0.71\\|18.71| = 18.71\\|46.71|= 46.71$

Calculate the mean of the above result to get the M.A.D

$Mean = \frac{\sum x}{n}$

$M.A.D = \frac{22.29+18.29+16.29+9.29+0.71+18.71+46.71}{7}\\M.A.D = \frac{132.29}{7}\\M.A.D = 18.8985714286\\M.A.D = 18.9$