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:
- How does the standard deviation help in understanding the data distribution?
- What is the difference between population standard deviation and sample standard deviation?
- How do you calculate variance from standard deviation?
- What are the advantages of using range vs. standard deviation for measuring spread?
- 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
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