Z - Score - Sports Stats

Lesson 9.2

Z - Scores

What is a z-score and Why do we use it?

• In order to compare different data sets we "standardize" the data so that is can be easily compared.

• Z-scores of data sets can be compared to other data sets.

Multiple Choice

In the formula for z-score what does the x stand for?

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Multiple Choice

In the formula for z-score what does the symbol below stand for?

 $\mu$  

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Multiple Choice

In the formula for z-score what does the symbol below stand for?

 $\sigma$  

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Z- SCORES

• They tell you how many Standard Deviations above or below the mean the given data point lies.

• Positive z - The point is above the Mean

• Negative z - The point is below the Mean

• z is 0 - The point is the same as the mean.

Multiple Choice

If the z - score is 1.5 the data point ________ the mean.

• above

• below

• the same as the mean

Multiple Choice

If the z - score is -1.5 the data point ________ the mean.

• above

• below

• the same as the mean

Multiple Choice

If the z - score is 0 the data point ________ the mean.

• above

• below

• the same as the mean

Example 1

• A student has gotten tests back in two classes. What can you conclude?

• The grade on the Math test was 82% the mean for the test 80 and the standard deviation 2.5.

• The grade on the Spanish test was 79% the mean for the test 75 and the standard deviation 4.

Example 2

• At a swim meet, a boy swam the 50 free in 29.52 seconds and 50 fly in 33.72. What can you conclude?

• The average times for 50 free has a mean of 31.2 with SD 2.1

• The average times for 50 fly has a mean of 39.11 with SD 3.7

Multiple Choice

When playing golf having a score with a negative z-score is better than a positive z-score.

• True

• False

Multiple Choice

When playing a Quizizz game having a score with a negative z-score is better than a positive z-score.

• True

• False

Multiple Choice

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Multiple Choice

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

Multiple Choice

Find the Z-score.

Mean = 27

Standard Deviation: 1.4

x = 11

• -11.43

• 7.85

• -2.33

• 4.16

Multiple Choice

Find the z-score.

Mean = 38

Standard Deviation: 1.2

x = 42

• 3.33

• -3

• 3.03

• -3.33