Math Problem Statement

The grade point averages​ (GPA) for 12 randomly selected college students are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. 2.5 3.2 2.6

1.7 0.9 4.0 2.3 1.2 3.7 0.2 2.4 3.4 Question content area bottom Part 1 ​(a) Find the sample mean. x overbarequals    2.34 ​(Round to two decimal places as​ needed.) Part 2 ​(b) Find the sample standard deviation. sequals    enter your response here ​(Round to two decimal places as​ needed.)

Solution

(a) The sample mean GPA is approximately 2.342.34 (rounded to two decimal places).

(b) The sample standard deviation is approximately 1.161.16 (rounded to two decimal places).

Would you like more details on how the calculations are done or have any questions?

Here are five related questions you might explore:

  1. How would you calculate the variance for this sample?
  2. How does changing the sample size affect the standard deviation?
  3. What is the difference between population standard deviation and sample standard deviation?
  4. How would the results change if one GPA was significantly higher or lower than the others?
  5. How can you use the standard deviation to analyze the spread of GPAs?

Tip: For sample standard deviation, always use n1n-1 (degrees of freedom) in the denominator to get an unbiased estimate.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Mean
Standard Deviation

Formulas

Sample mean: x̄ = (Σx) / n
Sample standard deviation: s = sqrt(Σ(xi - x̄)^2 / (n - 1))

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12 (or College Introductory Level)