1. Descriptive Statistics2
Descriptive Statistics
Elementary Statistics

2. Frequency Distributions and Their Graphs
Section 2.1
Frequency Distributions and Their Graphs

3. Frequency Distributions
Minutes Spent on the Phone
This data will be used for several examples. You might want to duplicate it for use with slides that follow.
Make a frequency distribution table with five classes.
Minimum value =
Maximum value = 67
Key values:
125

4. Steps to Construct a Frequency Distribution
1. Choose the number of classes
Should be between 5 and 15. (For this problem use 5)
2. Calculate the Class Width
Find the range = maximum value – minimum. Then divide
this by the number of classes. Finally, round up to a
convenient number. ( ) / 5 = Round up to 12.
3. Determine Class Limits
The lower class limit is the lowest data value that belongs in
a class and the upper class limit is the highest. Use the
minimum value as the lower class limit in the first class. (67)
4. Mark a tally | in appropriate class for each data value.
After all data values are tallied, count the tallies in each
class for the class frequencies.

5. Construct a Frequency Distribution
Minimum = 67, Maximum = 125
Number of classes = 5
Class width = 12 3 5 8 9
Class Limits Tally 78 90
102
114
126 67 79 91
103
115
Do all lower class limits first.

6. Frequency Histogram Boundaries Class 3 66.5 - 78.5 67 - 78 78.5 - 90.5
Class 3 5 8 9
Time on Phone 9 9 8 8 7 6 5 5 5
A histogram is a bar graph for which the bars touch. To form boundaries, find the distance between consecutive classes. Add half that distance to the lower limits and half to the upper limits. In this case the distance is 1 unit so add .5 to all upper limits and subtract .5 from all lower ones. The data must be quantitative. This histogram is labeled at the class boundaries. Explain that midpoints could have been labeled instead. 4 3 3 2 1 6 6 . 5 7 8 . 5 9 . 5 1 2 . 5 1 1 4 . 5 1 2 6 . 5
minutes

7. Other Information Midpoint: (lower limit + upper limit) / 2
Relative frequency: class frequency/total frequency
Cumulative frequency: number of values in that class or in lower
Class
Midpoint
Relative
Frequency
Cumulative
Frequency 3 5 8 9
72.5
84.5
96.5
108.5
120.5
0.10
0.17
0.27
0.30 3 8 16 25 30
The first two columns reflect the work done in previous slides. Once the first midpoint is calculated, the others can be found by adding the class width to the previous midpoint. Notice the last entry in the cumulative frequency column is equal to the total frequency.

8. Relative Frequency Histogram
Time on Phone
Relative frequency
A relative frequency histogram will have the same shape as a frequency histogram.
minutes
Relative frequency on vertical scale

9. More Graphs and Displays
Section 2.2
More Graphs and Displays

10. Stem-and-Leaf Plot
Lowest value is 67 and highest value is 125, so list stems from 6 to 12.
Stem
Leaf
6 |
7 |
8 |
9 |
10 |
11 |
12 | 6 2
Divide each data value into a stem and a leaf. The leaf is the rightmost significant digit. The stem consists of the digits to the left. The data shown represent the first line of the ‘minutes on phone’ data used earlier. The complete stem and leaf will be shown on the next slide. 2 8 3
To see complete display, go to next slide. 4

11. Stem-and-Leaf Plot Key: 6 | 7 means 67 6 | 7 7 | 1 8 8 | 2 5 6 7 7
6 | 7
7 | 1 8
8 |
9 |
10 |
11 | 2 6 8
12 | 2 4 5
Key: 6 | 7 means 67
Stress the importance of using a key to explain the plot. 6|7 could mean 6700 or .067 for a different problem. A stem and leaf should not be used with data when values are very different such as 3, 34,900, 24 etc. The stem-and leaf has the advantage over a histogram of retaining the original values.

12. NASA budget (billions of $) divided among 3 categories.
Pie Chart
Used to describe parts of a whole
Central Angle for each segment
NASA budget (billions of $) divided among 3 categories.
Pie charts help visualize the relative proportion of each category. Find the relative frequency for each category and multiply it by 360 degrees to find the central angle.
Billions of $
Human Space Flight
Technology
Mission Support
Construct a pie chart for the data.

13. Pie Chart Human Space Flight 5.7 143 Technology 5.9 149
Billions of $
Degrees
Human Space Flight
5.7
143
Technology
5.9
149
Mission Support
2.7 68
14.3
360
Total
Mission
Support
19%
Human
Space Flight
40%
NASA Budget
(Billions of $)
Technology
41%