Question

The following data give the prices of seven textbooks randomly selected from a university bookstore. $92 $176 $102 $126 $55 $155 $148 a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero? Mean = $ 122 Deviation from the mean for $176- sum of these deviations b. Calculate the range, variance, and standard deviation. [Round your answers to 2 decimal places.] Range = $ Variance Standard deviation $

Answer 1

(a)

(i)

Mean ($\bar{x}$) is given by:

$\bar{x}=\frac{\sum_{i=1}^{7}x_{i}}{7}=\frac{854}{7}=122$

(ii)

Deviation from the mean for $176 = 176 - 122 = 54

(iii)

To find the sum of these deviations:

x	x - $\bar{x}$
92	- 30
176	54
102	- 20
126	4
55	- 67
155	33
148	26
Total =	0

Thus, we get
Sum of these deviations = 0

(b)

(i)

Range = Maximum -Minimum = 176 - 55 = 121.00

(ii)

To find Variance:

x	x - $\bar{x}$	(x - $\bar{x}$)2
92	- 30	900
176	54	2916
102	- 20	400
126	4	16
55	- 67	4489
155	33	1089
148	26	676
Total =	0	10486

Variance (s²) is given by:

$s^{2}=\frac{\sum_{i=1}^{7}(x_{i}-\bar{x})^{2}}{6}=\frac{10486}{6}=1747.67$

(iii)

Standard deviation (s) is given by:

$s=\sqrt{1747.67}=41.81$