Math Problem Statement

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

43

71

36

86

61

79

24

52

40

70

32

74

37

80

40

83

26

89

32

63

80

96

15

Range = 

Standard Deviation =

Solution

numpy as np

Data from the given table

tv_hours = [70, 43, 71, 36, 86, 61, 79, 24, 52, 40, 70, 32, 74, 37, 80, 40, 83, 26, 89, 32, 63, 80, 96, 15]

Calculating range and standard deviation

range_tv = max(tv_hours) - min(tv_hours) std_dev_tv = round(np.std(tv_hours, ddof=1), 2)

range_tv, std_dev_tvThe range and standard deviation for the data are as follows:

  • Range = 81
  • Standard Deviation = 23.94

Would you like a detailed explanation of how these values were calculated? Here are some related questions you might find interesting:

  1. How does the standard deviation help in understanding the data distribution?
  2. What is the difference between population standard deviation and sample standard deviation?
  3. How do you calculate variance from standard deviation?
  4. What are the advantages of using range vs. standard deviation for measuring spread?
  5. How can the range or standard deviation be influenced by outliers?

Tip: When interpreting standard deviation, a larger value indicates that the data points are more spread out from the mean, whereas a smaller value suggests they are closer to the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Range
Standard Deviation

Formulas

Range = max(data) - min(data)
Standard Deviation = sqrt( Σ(xi - mean)² / (n-1) )

Theorems

Empirical Rule
Chebyshev's Theorem

Suitable Grade Level

Grades 9-12