Math Problem Statement

A random sample of 10 subjects have weights with a standard deviation of 12.2207 kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result.

Solution

To find the variance, you use the formula:

Variance=(Standard Deviation)2\text{Variance} = (\text{Standard Deviation})^2

Given:

  • Standard Deviation = 12.2207 kg

So, the variance will be:

Variance=(12.2207kg)2\text{Variance} = (12.2207 \, \text{kg})^2

Now, let's calculate it.The variance of the weights is 149.3455kg2149.3455 \, \text{kg}^2.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

  1. What is the difference between standard deviation and variance?
  2. How would you interpret a high variance versus a low variance in a dataset?
  3. What is the formula for the variance of a population as opposed to a sample?
  4. How would the variance change if we doubled the standard deviation?
  5. Can you explain why variance has squared units compared to standard deviation?

Tip: Remember that variance is always in squared units of the original data, which often makes it less intuitive than the standard deviation when interpreting data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Variance
Standard Deviation

Formulas

Variance = (Standard Deviation)^2

Theorems

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Suitable Grade Level

Grades 9-11