Question 1 (2 points)
What are measures of variance and what kind of information do they give us when working with sets of numbers?

B

It is a single number used to describe how much variation there is in a distribution.
Information on how scores are spread from the center of a distribution

Ask by Curry Park. in the United States

Mar 26,2025

Question

Question 1 (2 points)
What are measures of variance and what kind of information do they give us when working with sets of numbers?

B

It is a single number used to describe how much variation there is in a distribution.
Information on how scores are spread from the center of a distribution

Ask by Curry Park. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1. **Definition of Variance Measures:**  
   Measures of variance quantify how much the numbers in a set differ from the center (usually the mean). One common measure is the variance, denoted as $$ \sigma^2 $$ for a population or $$ s^2 $$ for a sample. It is computed as the average of the squared differences from the mean.

2. **Computation:**  
   For a set of $$ n $$ numbers $$ x_1, x_2, \ldots, x_n $$ with mean $$ \bar{x} $$, the sample variance is given by  
   $$
   s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i-\bar{x})^2.
   $$
   The population variance is similarly given by  
   $$
   \sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i-\mu)^2,
   $$
   where $$ \mu $$ is the population mean.

3. **Additional Measures of Spread:**  
   A related measure is the standard deviation, $$ s $$ or $$ \sigma $$, which is the square root of the variance. It provides a measure of spread in the same units as the data.

4. **Information Provided:**  
   Measures of variance, such as the variance and standard deviation, inform us about:
   - **Spread of Data:** They indicate how widely the scores are spread around the center.
   - **Consistency:** A smaller variance means that the numbers are closer to the mean, showing more consistency among data points.
   - **Variability:** A larger variance indicates more variability, meaning the data points are more dispersed.

Thus, variance gives us a single number that describes how much variation there is in a distribution, highlighting how scores are spread from the center of a distribution.
Measures of variance, like variance and standard deviation, show how much the numbers in a set differ from the center. They tell us about the spread of data, consistency of scores, and how much variability there is in the distribution.

Question 1 (2 points)
What are measures of variance and what kind of information do they give us when working with sets of numbers?

B

It is a single number used to describe how much variation there is in a distribution.
Information on how scores are spread from the center of a distribution

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Question 1 (2 points) What are measures of variance and what kind of information do they give us when working with sets of numbers? B It is a single number used to describe how much variation there is in a distribution. Information on how scores are spread from the center of a distribution

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Latest Statistics Questions

Question 1 (2 points)
What are measures of variance and what kind of information do they give us when working with sets of numbers?

B

It is a single number used to describe how much variation there is in a distribution.
Information on how scores are spread from the center of a distribution