Interpreting Descriptive Statistics
Standard deviation tells us the average distance data values fall from the mean.
 If the standard deviation is ________ then the data is close together.
 If the standard deviation is ________ then the data is spread out.
Normal resting pulse rate for a teenager is between 60 – 90 beats per minute. (Livestrong.com)
The following graph represents a class of 15 students with a pulse rate mean of 75 and standard
deviation of 8.944.
Pulse Rate of Algebra Class
55
60
65
70
75
80
85
90
Example:
How many students fall within 1 standard
deviation of the mean?
95
A z-score tells us how many standard deviations a value falls away from the mean.
 Calculate a value’s z-score using the formula: z 
x

meaning z-score =
data value - mean
standard deviation
Example: What is the z-score for a pulse rate of 85? Does this pulse rate fall within 1 standard deviation
of the mean? Is it above or below?
Example: What is the z-score for your pulse rate? Within how many standard deviations of the mean do
you fall?
If the z-score is _____________________ then the value falls above the mean.
If the z-score is _____________________ then the value falls below the mean.
Interpreting Descriptive Statistics
Descriptive statistics for two data sets are shown below:
Data Set A
Data Set B
Mean = 83
Mean = 83
Absolute Mean Deviation = 7.68
Absolute Mean Deviation = 10.24
Variance = 94.96
Variance = 219.04
Standard Deviation = 9.74
Standard Deviation = 14.8
1. Which histogram below matches the descriptive statistics of data set A, and which matches
the descriptive statistics of data set B? How do you know?
Mrs. Smith's 1st Block Test Scores
8
Test Scores of Mrs. Smith’s
Second Block Class
8
7
7
6
6
5
5
Frequency
Frequency
Mrs. Smith's 2nd Block Test Scores
Test Scores of Mrs. Smith’s
First Block Class
4
3
4
3
2
2
1
1
0
0
29-36
37-44
45-52
53-60
61-68
69-76
77-84
85-92
93-100
Test Scores
DATA SET ______
29-36
37-44
45-52
53-60
61-68
69-76
77-84
85-92
Test Scores
DATA SET ______
2. Which of the two histograms contains an outlier(s)?
How do you know?
3. Examine the absolute mean deviation and the standard deviation of both data sets. Which
measure of dispersion was least affected by the outlier(s)?
How do you know?
4. How many elements in data set A fall within one standard deviation above the mean?
How do you know?
5. What is the z-score for the element 91 in data set B?
6. In a set of test scores, an 89 has a z-score of 1.5, and a 93 has a z-score of 2. What is the
mean test score? _________________ What is the standard deviation?
93-100