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 15.0215.02.

Would you like further details on how this was calculated, or have any questions?

Here are 5 related questions for practice:

  1. How is the sample standard deviation different from the population standard deviation?
  2. What does the standard deviation tell you about the spread of the data?
  3. How would the standard deviation change if the largest value increased significantly?
  4. Can you find the mean of this data set?
  5. 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