Standard Deviation and Z-Score

Standard Deviation

Read each slide carefully before continuing through the lesson

Definition

Which set of data has data points that are closer to the mean?

Multiple Choice

List each set of data by color from the lowest standard deviation to the highest standard deviation.

• blue, green, pink, red

• red, pink, green, blue

• pink, green, red, blue

• blue, green, red, pink

Multiple Choice

Look at each data set's standard deviation.

Set 1: 15.9

Set 2: 14.64

Set 3: 17.88

Which set of data has values that are closer in relation to the mean value of the data?

• Set 1

• Set 2

• Set 3

• Not enough information is provided

Characteristics of the Normal Curve

• MEAN = MEDIAN = Mode: The mean and the median are the same

  • located in the center of the curve. 50% of the data is above or below

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