Question

question 11
the table below gives the number of hours spent watching tv last week by a sample of 24 children.
56 59 28 74 62 46
75 32 57 56 35 48
35 39 82 90 60 35
53 42 28 40 96 14
a. range =
b. standard deviation =
round your answers to the nearest hundredth as needed.
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Explanation:

Step1: Find the range

The range is calculated by subtracting the minimum value from the maximum value.
First, find the maximum value in the data set: \(96\)
Then, find the minimum value in the data set: \(14\)

$$ \text{Range}=96 - 14 $$

$$ \text{Range}=82 $$

Step2: Find the standard deviation

1. Calculate the mean \(\bar{x}\) of the data set.

The sum of all data values \(S=\sum x=56 + 59+28+74+62+46+75+32+57+56+35+48+35+39+82+90+60+35+53+42+28+40+96+14\)

$$ S = 1274 $$

The number of data points \(n = 24\)

$$ \bar{x}=\frac{S}{n}=\frac{1274}{24}\approx53.08 $$

1. Calculate the variance \(s^{2}\)

$$ s^{2}=\frac{\sum(x - \bar{x})^{2}}{n-1} $$

$$
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$$ s^{2}=\frac{7992.96}{23}\approx347.52 $$

1. Calculate the standard deviation \(s\)

$$ s=\sqrt{s^{2}}=\sqrt{347.52}\approx18.64 $$

Answer:

a. \(82\)
b. \(18.64\)