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 (ss) = 13.2965 kg

The formula for variance (s2s^2) is:

s2=(13.2965kg)2s^2 = (13.2965 \, \text{kg})^2

Now, calculate the variance:

s2=13.29652=176.7504kg2s^2 = 13.2965^2 = 176.7504 \, \text{kg}^2

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:

  1. How is the variance related to the standard deviation?
  2. What is the significance of variance in statistical analysis?
  3. How would you interpret a higher or lower variance in a data set?
  4. Can variance ever be negative? Why or why not?
  5. 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!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Variance
Standard Deviation

Formulas

Variance formula: s^2 = (standard deviation)^2

Theorems

-

Suitable Grade Level

Grades 11-12