Math Problem Statement
A random sample of 10 subjects have weights with a standard deviation of 13.2965 kg. What is the variance of their weights? Be sure to include the appropriate units with the result. Question content area bottom Part 1 The variance of the sample data is enter your response here ▼ kg cubed . kg squared . kg. (Round to four decimal places as needed.)
Solution
To find the variance of the sample data, you square the standard deviation.
Given:
- Standard deviation () = 13.2965 kg
The formula for variance () is:
Now, calculate the variance:
So, the variance of the sample data is 176.7504 kg².
Would you like further details or have any questions?
Here are 5 related questions:
- How is the variance related to the standard deviation?
- What is the significance of variance in statistical analysis?
- How would you interpret a higher or lower variance in a data set?
- Can variance ever be negative? Why or why not?
- How does variance differ between a sample and a population?
Tip: Always remember that the variance is the square of the standard deviation, so its units are squared as well!
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Math Problem Analysis
Mathematical Concepts
Statistics
Variance
Standard Deviation
Formulas
Variance formula: s^2 = (standard deviation)^2
Theorems
-
Suitable Grade Level
Grades 11-12
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