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 22 80 28 52 58
87 22 39 73 72 52
82 52 40 88 61 69
43 43 84 28 99 16
range =
standard deviation =

Explanation:

Step1: Find min and max values

Min = 16, Max = 99

Step2: Calculate range

$\text{Range} = \text{Max} - \text{Min} = 99 - 16$

Step3: Calculate sample mean

First sum all values:
$44+22+80+28+52+58+87+22+39+73+72+52+82+52+40+88+61+69+43+43+84+28+99+16 = 1393$
$\bar{x} = \frac{1393}{24} \approx 58.0417$

Step4: Calculate sample standard deviation

Use formula $s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}}$. Using technology to compute the sum of squared deviations and the root:
$s \approx 24.37$

Answer:

Range = 83
Standard Deviation = 24.37