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:
- (mean) = 44.11 (rounded to two decimal places)
- (standard deviation) = 13.04
- (variance) = 170.16
Would you like a detailed breakdown of how these were calculated?
Here are five related questions:
- How would adding an outlier affect the mean and standard deviation?
- What is the difference between population and sample standard deviation?
- How can you use standard deviation to assess data spread?
- How does variance help in understanding data distribution?
- 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.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Mean, Standard Deviation, and Variance Calculation for Sample Data
Calculating Sample Mean and Sample Standard Deviation for Data Set
Statistical Analysis: Mean, Median, Mode, Range, and Standard Deviation of a Data Set
Calculate Sample Mean, Standard Deviation, and Population Standard Deviation for Given Data
Find Range, Mean, Median, Mode, and Standard Deviation of a Data Set