Math Problem Statement

Find x bar, s, and s^2 for the following data set: 20, 45, 42, 52, 65, 20, 60, 49, 24, 37, 23, 24, 50, 59, 62, 45, 52, 61, 41, 25, 28, 27, 50, 47, 58, 40, 42, 48, 40, 45, 39, 55, 50, 55, 48, 60

Solution

For the given data set, the results are as follows:

  • xˉ\bar{x} (mean) = 44.11 (rounded to two decimal places)
  • ss (standard deviation) = 13.04
  • s2s^2 (variance) = 170.16

Would you like a detailed breakdown of how these were calculated?

Here are five related questions:

  1. How would adding an outlier affect the mean and standard deviation?
  2. What is the difference between population and sample standard deviation?
  3. How can you use standard deviation to assess data spread?
  4. How does variance help in understanding data distribution?
  5. What role does the mean play in determining data symmetry?

Tip: Always use sample standard deviation (n-1) when working with a subset of data rather than the entire population.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Mean
Variance
Standard Deviation

Formulas

Mean (x̄) = (Σx) / n
Variance (s^2) = Σ(x - x̄)^2 / (n - 1)
Standard Deviation (s) = √Variance

Theorems

Central Limit Theorem (relevant in understanding sample distributions)

Suitable Grade Level

Grades 10-12