Answer
(a)Range $=25$
(b)Standard Deviation $=9.27$
Work Step by Step
$$\text{Solution}$$
Given Information:
Data Set ⟹ $(40, 35, 45, 55, 60)$
Total Number of Items in Data Set $n=5$
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:
Range Standard Deviation
Answer:
(a) To Find Range:
Re-Arrange the Given Data Set in Ascending Order
$$35, 40,45,55,60$$
$$\text{Range = Highest Value - Lowest Value}$$
$$ \text{Range} = 60-35$$
$$\text{Range} =25$$
(b) To Find Standard Deviation:
Re-Arrange the Given Data Set in Ascending Order
$$35, 40,45,55,60$$
Mean = $\frac{35+40 +45 +55 +60}{5}$
Mean = $\frac{3235}{5}$
Mean= $\mu$ = $47 $
$x_i=35,40,45,55,60 $
$|x_i-\mu|= 12,7,2,8,13 $
$|x_i-\mu|^2$= $144,49,4,64,169 $
Standard Deviation $=\sigma =$ $\frac{\sqrt {\Sigma (|x_i- \mu|)^2}}{n}$
$=\sigma $ = $\sqrt{\frac{144+49+4+64+169}{5}}$
$=\sigma $= $\sqrt{\frac{430}{5}}$
$=\sigma $ = $\sqrt {86}$
$=\sigma $ = $9.27$
