Measures of Variability: Variance

Presentation

•

Mathematics

•

11th - 12th Grade

•

Medium

•

CCSS

6.SP.B.5C, 6.SP.B.5A, 7.SP.B.3

Standards-aligned

Elizabeth Borres

Used 6+ times

FREE Resource

13 Slides • 17 Questions

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

Multiple Choice

What is the interquartile range of the data set below?

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

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?

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

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?

Type response here

Poll

Ready for the next lesson?

Yes

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}

Type response here

Open Ended

What do you think is the first step?

Type response here

Step 1: Find the mean.

Add all the numbers and divide by the total.

Fill in the Blanks

Type answer...

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)?

8.13

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.

Type response here

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?

Type response here

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.

Type response here

Measures of Variability: Variance

by: Ph-USA Guru

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