Math Problem Statement
Find the population standard deviation of 51, 58, 59, 62, 63, 64, 64, 65, 65, 66, 67, 71, 74, 75, 75, 77, 78, 79, 82, 82, 83, 86, 89, 89, 89, 90, 93, 94, 95, 96, 101, 105, 116
Solution
The population standard deviation of the given data set is approximately .
Would you like further details on how this was calculated, or have any questions?
Here are 5 related questions for practice:
- How is the sample standard deviation different from the population standard deviation?
- What does the standard deviation tell you about the spread of the data?
- How would the standard deviation change if the largest value increased significantly?
- Can you find the mean of this data set?
- How is variance related to standard deviation?
Tip: The population standard deviation divides by the total number of data points, while the sample standard deviation divides by the number of data points minus one.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Population Standard Deviation
Formulas
Population standard deviation formula: \( \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \)
Theorems
Standard Deviation Theorem
Suitable Grade Level
Grades 10-12
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