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 (rounded to two decimal places).
(b) The sample standard deviation is approximately (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:
- How would you calculate the variance for this sample?
- How does changing the sample size affect the standard deviation?
- What is the difference between population standard deviation and sample standard deviation?
- How would the results change if one GPA was significantly higher or lower than the others?
- How can you use the standard deviation to analyze the spread of GPAs?
Tip: For sample standard deviation, always use (degrees of freedom) in the denominator to get an unbiased estimate.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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)
Related Recommendation
Calculate the Sample Mean for College GPAs: Step-by-Step
How to Calculate the Sample Mean for GPA Data
Calculating GPA Percentiles and Quartiles in a Normal Distribution
Calculating Sample Mean, Standard Deviation, and Confidence Interval for Test Scores
Calculating 95% and 99% Confidence Intervals for Population Mean