Question

question 9
using technology, find the range and standard deviation. round to two decimals places.
the table below gives the number of hours spent watching tv last week by a sample of 24 children.
44 86 67 22 66 47
32 40 56 66 32 39
46 60 25 54 65 53
42 60 54 42 93 19
range =
standard deviation =

Explanation:

Step1: Find min and max values

Min value = 19, Max value = 93

Step2: Calculate the range

Range = Max - Min = $93 - 19$

Step3: Calculate sample mean

First sum all values:
$44+86+67+22+66+47+32+40+56+66+32+39+46+60+25+54+65+53+42+60+54+42+93+19 = 1260$
Mean $\bar{x} = \frac{1260}{24} = 52.5$

Step4: Calculate sample standard deviation

Use formula $s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}}$
Compute squared deviations, sum them:
$\sum(x_i - 52.5)^2 = 8956$
$s = \sqrt{\frac{8956}{24-1}} = \sqrt{\frac{8956}{23}}$

Answer:

Range = 74
Standard Deviation = 19.77