Question

the table below gives the number of hours spent watching tv last week by a sample of 24 children.
78 67 56 23 84 84
29 32 54 83 71 46
73 87 35 59 85 38
21 34 46 74 98 10
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: \(98\)
Then, find the minimum value in the data set: \(10\)

$$ \text{Range}=98 - 10 $$

$$ \text{Range}=88 $$

Step2: Find the standard deviation

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

$$ \bar{x}=\frac{78 + 67+56+23+84+84+29+32+54+83+71+46+73+87+35+59+85+38+21+34+46+74+98+10}{24} $$

$$ \bar{x}=\frac{1445}{24}\approx60.21 $$

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

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

$$
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$$ s^{2}=\frac{13391.96}{23}\approx582.26 $$

1. Calculate the standard deviation \(s\)

$$ s=\sqrt{s^{2}}=\sqrt{582.26}\approx24.13 $$

Answer:

a. \(88\)
b. \(24.13\)