Answer
Range $=25$
Standard Deviation $=9.24$
Work Step by Step
$$\text{Solution}$$
Given Information:
Data Set ⟹ $(141, 116, 117, 135, 126, 121) $
Total Number of Items in Data Set $n=6$
Formula:
Range = Highest Value - Lowest Value
Standard Deviation $=\sigma =$ $\frac{\sqrt {\Sigma (|x_i- \mu|)^2}}{n}$
Mean = $\frac {\text{Sum of All Values}}{\text{Total Number of Values}}$
To Find:
a)Range
b)Standard Deviation
Answer:
(a) To Find Range:
Re-Arrange the Given Data Set in Ascending Order
$$116, 117, 121, 126, 135, 141$$
$$\text{Range = Highest Value - Lowest Value}$$
$$ \text{Range} = 141-116 = 25$$
$$\text{Range} =25$$
(b) To Find Standard Deviation:
Re-Arrange the Given Data Set in Ascending Order
$$116, 117, 121, 126, 135, 141$$
Mean = $\frac{141+116+117+135+126+121}{6}$
Mean = $\frac{756}{6}$
Mean= $\mu$ = $126 $
$x_i=116, 117, 121, 126, 135, 141 $
$|x_i-\mu|= 10,9,5,0,9,15 $
$|x_i-\mu|^2$= $100,81,25,0,81,225 $
Standard Deviation $=\sigma =$ $\frac{\sqrt {\Sigma (|x_i- \mu|)^2}}{n}$
$=\sigma $ = $\sqrt{\frac{100+81+25+0+81+225}{6}}$
$=\sigma $= $\sqrt{\frac{512}{6}}$
$=\sigma $ = $\sqrt {85.33}$
$=\sigma $ = $9.24$
