The table below gives the number of hours spent watching TV last week by a sample of 24 children.

30

41

46

75

84

41

58

66

71

62

31

25

77

28

38

52

47

87

25

40

73

76

95

15

Range =

Standard Deviation =

Let's first calculate the **range** and then the **standard deviation** for the given data set of TV watching hours.

### Data Set:
\[ 30, 41, 46, 75, 84, 41, 58, 66, 71, 62, 31, 25, 77, 28, 38, 52, 47, 87, 25, 40, 73, 76, 95, 15 \]

### 1. Range:
The **range** is the difference between the maximum and minimum values in the data set.

- Maximum value = 95
- Minimum value = 15

\[
\text{Range} = \text{Max} - \text{Min} = 95 - 15 = 80
\]

So, the **range** is **80**.

### 2. Standard Deviation:
The formula for the standard deviation for a sample is:

\[
s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}
\]

Where:
- \( n \) = number of data points (here \( n = 24 \))
- \( x_i \) = each individual data point
- \( \overline{x} \) = sample mean

Let's calculate the **mean** first:

\[
\overline{x} = \frac{\sum x_i}{n} = \frac{30 + 41 + 46 + 75 + 84 + 41 + 58 + 66 + 71 + 62 + 31 + 25 + 77 + 28 + 38 + 52 + 47 + 87 + 25 + 40 + 73 + 76 + 95 + 15}{24}
\]

\[
\overline{x} = \frac{1363}{24} = 56.79 \ (\text{rounded to 2 decimal places})
\]

Now, we calculate the squared deviations from the mean for each data point and sum them:

\[
\sum (x_i - \overline{x})^2 = (30 - 56.79)^2 + (41 - 56.79)^2 + \ldots + (15 - 56.79)^2
\]

I will compute the standard deviation based on this.

The sample mean of the data set is approximately **53.46** hours, and the **standard deviation** is approximately **22.73** hours.

### Summary:
- **Range**: 80
- **Standard Deviation**: 22.73

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. How would the range and standard deviation change if one more child watched 100 hours of TV?
2. What is the variance of the data set (square of the standard deviation)?
3. How would you interpret the meaning of the standard deviation in this context?
4. What percentage of data points falls within one standard deviation of the mean?
5. How would removing an outlier, such as 95, affect the standard deviation?

**Tip**: The range gives you a quick sense of data spread, but standard deviation provides a deeper understanding of how values deviate from the mean.

The table below gives the number of hours spent watching TV last week by a sample of 24 children. 30, 41, 46, 75, 84, 41, 58, 66, 71, 62, 31, 25, 77, 28, 38, 52, 47, 87, 25, 40, 73, 76, 95, 15. Find the Range and Standard Deviation.

Learn how to calculate the range and standard deviation for a dataset of TV watching hours for 24 children. The dataset includes values like 30, 41, 46, 75, and more. We provide a step-by-step solution covering statistical measures of dispersion, including the formula for standard deviation. Suitable for students in Grades 9-11.

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