Question

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.
70 57 47 82 69 33
37 41 67 24 51 39
23 81 58 27 41 64
69 55 55 64 94 12
range =
standard deviation =

Explanation:

Step1: Identify min and max values

Data set: 70,57,47,82,69,33,37,41,67,24,51,39,23,81,58,27,41,64,69,55,55,64,94,12
Min = 12, Max = 94

Step2: Calculate the range

Range = Max - Min
$\text{Range} = 94 - 12$

Step3: Calculate sample mean

First sum all values:
$70+57+47+82+69+33+37+41+67+24+51+39+23+81+58+27+41+64+69+55+55+64+94+12 = 1340$
Mean $\bar{x} = \frac{1340}{24} \approx 55.8333$

Step4: Calculate sample standard deviation

Use sample standard deviation 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 solve:
$\sum_{i=1}^{24}(x_i - 55.8333)^2 \approx 12698.6667$
$s = \sqrt{\frac{12698.6667}{23}} \approx \sqrt{552.1159} \approx 23.50$

Answer:

Range = 82
Standard Deviation = 23.50