Measures of Variability: Variance

Measures of Variability: Variance

by: Ph-USA Guru

What you'll learn today?

• Review how to find the mean, mean absolute deviation (MAD), and Interquartile range (IQR).

• Calculate the population and sample variance.

• Apply the measures of variability in real life scenario (grades)

Multiple Choice

Find the interquartile range using the following.

Minimum: 1

Q1: 3

Median: 5

Q3: 7

Maximum: 9

• 8

• 4

• 5

• 10

Multiple Choice

What is the interquartile range of the data set below?

3, 5, 6, 6, 7, 8, 9

• 3

• 6

• 2

• 8

Multiple Choice

The data below shows the number of hours boys and girls spent studying for a test.

Boys: {2, 1, 3, 1, 2, 2}

Girls: {4, 1, 3, 2, 2, 4}

What is the difference in the interquartile range between the girls and boys?

• 1

• 2

• 3

• 5

Multiple Select

True or False

To find the IQR (interquartile range) you have to add the Q3 + Q1.

• True

• False

Multiple Select

find the lower quartile of the following set of scores12, 9, 4, 6, 5, 8, 9, 4, 10, 2

• 10

• 4

• 9

• 6

Multiple Select

What are the 3 measures of variability that we have discussed?

• Range

• Mean Absolute Deviation

• Interquartile Range

• Variance

Open Ended

Before we proceed to the next measure, do you have any clarification/question about the previous lesson?

Poll

Ready for the next lesson?

• Yes

• No

Measures of Variability

• Range

• Mean Absolute Deviation (MAD)

• Interquartile Range (IQR)

• Variance (TODAY)

VARIANCE

• A measure of how data points differ from the mean.

• Gets rid of the positive and negative values in our “Difference from Mean” column before that added up to 0.

• However, because we’re squaring our values they will not be in the metric of our original scale.

• If we calculate the variance for a test out of 100, a variance of 100 is actually average variability of 10 pts. (Ö100 = 10) about the mean of the test

Formula for VARIANCE

COPY!!! COPY!!!COPY!!!

Open Ended

What have you noticed with the formula? Compare.

VARIANCE:

 $Population\ Variance:\ \ \ \ \ \ \ \sigma\ =\ \frac{\Sigma\left(X\ -\ \overline{X}\right)^2}{N}$  
 $Sample\ Variance\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ s=\frac{\Sigma\left(X\ -\ \overline{X}\right)^2}{N\ -\ 1}$  

 $MAD\ =\ \frac{\Sigma\left|X-\overline{X}\right|}{N}$  

Open Ended

What do you think is the first step?

Step 1: Find the mean.

• Add all the numbers and divide by the total.

Fill in the Blanks

What is the mean? Round your answer to whole number.

Step 2: Subtract the mean from each score and the absolute value. Then add.

• 3 - 12 = -9 = 9

• 5-12 = -7 = 7

• ....

Step 2: Subtract the mean from each score and the absolute value. Then add.

• 3 - 12 = -9 = 9

• 5-12 = -7 = 7

• ....

Multiple Choice

What is the Mean Absolute Deviation (MAD)?

• 8.

• 8.13

• 8.33

• 8.44

Open Ended

Before we proceed to the next slide, type 1 if no question.If there is, please type your question or unmute yourself if you have clarifications.

How to find the VARIANCE?

• Population Variance

• Sample Variance

• Just get the square each value on the 3rd column. Then add.

Multiple Choice

 $\sigma\ =\ \frac{\Sigma\left(X\ -\ \overline{X}\right)^2}{N}$  

What is the population variance? Use the formula above. 

• 130.33

• 131.33

• 132.33

• 133.33

Open Ended

Question?Clarification?

Multiple Choice

 $s\ =\ \frac{\Sigma\left(X\ -\ \overline{X}\right)^2}{N\ -\ 1}$  

What is the sample variance? Use the formula above. 

• 157.3

• 157.4

• 157.5

• 157.6

Open Ended

If you don't have question, explain how to find the variance.