Grade 9 Math: Understanding Variance

Grade 9 Math: Understanding Variance

Learning goal and worked example

Calculate population variance and distinguish it from sample variance.

For the population {1,3,5}, the mean is 3. Squared deviations are 4,0,4, so variance = 8/3. Dividing by 2 instead would give the sample variance, 4.

Extension: use after mean and squared deviations; population and sample formulas may be beyond your Grade 9 syllabus.

Read each question carefully and answer to the best of your ability. Show all your work for calculation problems.

1. Which of the following best describes variance?

2. What is the symbol commonly used to represent population variance?

1. Variance is calculated by taking the average of the   from the mean.

2. The square root of the variance is known as the  .

3. A high variance indicates that data points are   from the mean, while a low variance indicates they are   to the mean.

1. Explain why we square the differences from the mean when calculating variance.

2. What is the main difference between population variance and sample variance?

1. Variance can never be a negative value.

2. Standard deviation is always smaller than variance.

Treat these five values as the complete population. Calculate the population variance (divide by N = 5):

Dataset: {2, 4, 6, 8, 10}

The five study-hour values are 1, 2, 3, 1, 4 hours, also shown below. Treat these five students as the complete population and calculate the population variance.