Question

Find:

a. the mean
b. the deviation from the mean for each data item.
c. the sum of the deviations in part b.

147, 154, 156, 161, 162

Answer 1

Answer:

Step-by-step explanation:

Given the dataset 147, 154, 156, 161, 162,

Mean is the sum of the dataset divided by the total number of dataset.

a) Mean = $\sum Xi/N$

$\overline x = \dfrac{147+154+156+161+162}{5}\\ \\\overline x = \dfrac{780}{5}\\ \\\overline x= 156$

b) The formula for calculating the deviation from the mean for each value is expressed as $Xi - \overline X$ where;

Xi is value of each item

xbar is the mean = 156

Mean deviation of 147 = 147-156 = -9

Mean deviation of 154 = 154-156 = -2

Mean deviation of 156 = 156-156 = 0

Mean deviation of 161 = 161-156 = 5

Mean deviation of 162 = 162-156 = 6

c) Sum of the deviations $\sum Xi - \overline X$ = (-9-2+0+5+6)

$\sum Xi - \overline X$ = -11+11

$\sum Xi - \overline X$ = 0

Hence the sum of deviation from the mean is 0