Unit 3 Standard Deviation

Variability What is it?

Consistency What is it?

Variability high or low?

Consistency high or low?

Variability high or low?

Consistency high or low?

Variability high or low?

Consistency high or low?

Variability high or low?

Consistency high or low?

High Variability Low Consistency

High Consistency Low Variability

Deviation What is it?

Small Standard Deviation Low Variability & High Consistency

Large Standard Deviation High Variability & Low Consistency

High High High variability and low consistency Review 1. You go to the grocery store to pick up some fruits and veggies. Would you expect the selection to have a high level of variability or low? High 2. When you get in the car, you turn the radio to your favorite station. Is there a high or low consistency in the type of music played on that station? High 3. Describe the variability and consistency of the following: the math grades of all the 10th grade students at Hillgrove High variability and low consistency

Standard Deviation

Find the Standard Deviation Use the calculator handout to help you put the data in! 12, 12, 57, 26, 9, 16, 18, 21, 25, 18, 5

What is the Mean of the math test scores of these two classes? Class A Class B 57 65 83 94 95 96 98 93 71 63 72 76 80 81 83 84 85 89

Since the averages are the same, can we assume that the students in both classes all did pretty much the same on the exam?

The answer is… No. The average (mean) does not tell us anything about the distribution or variation in the grades.

So, we need to come up with some way of measuring not just the average, but also the spread of the distribution of our data.

Find the Standard Deviation the math test scores of these two classes Class A Class B 57 65 83 94 95 96 98 93 71 63 72 76 80 81 83 84 85 89

Mean Alice’s Test Scores: 72, 100, 56, 60, 64, 74, 78 Sam’s Test Scores: 71, 74, 71, 66, 74, 76

Alice’s Test Scores: 72, 100, 56, 60, 64, 74, 78 Describe her grades.

Sam’s Test Scores: 71, 74, 71, 66, 74, 76 Describe his grades.

Alice’s Test Scores: 72, 100, 56, 60, 64, 74, 78 Sam’s Test Scores: 71, 74, 71, 66, 74, 76 Who’s grade is more consistent? Who’s grade is more variable? Who is the better student?

Example 2: Find the Mean and Standard Deviation Xi F1 = frequency 10 4 8 5 6 2

Example 3: Find the Mean and Standard Deviation Xi FRQ 1 2 3 4 5 6 7 8

Example 4: Find the Mean and Standard Deviation

Workbook pages 272 & 273 #1-13 ONLY Find mean and standard deviation