1. Statistics Describing Data Using Tables and Graphs
Assignment 2
Example Problems

2. Frequency Distributions
Objective: Identify the class width, class midpoints, and class boundaries for the given frequency distribution
Daily Low Temperature (°F)
Frequency
50-53 1
54-57 3
58-61 5
62-65 11
66-69 7
70-73
74-77

3. Frequency Distributions
Class width is the difference between two consecutive lower class limits or two consecutive lower class boundaries and thus 53, 52, 51, 50 is a width of 4
Daily Low Temperature (°F)
Frequency
50-53 1
54-57 3
58-61 5
62-65 11
66-69 7
70-73
74-77

4. Frequency Distributions
Class midpoints are the values in the middle of the class. Because there is no “exact” middle we find by averaging the class width, that is (53-50)/2 = 1.5
So each lower value, add 1.5 to get the midpoints of
51.5
55.5
59.5
63.5
67.5
71.5
75.5
Daily Low Temperature (°F)
Frequency
50-53 1
54-57 3
58-61 5
62-65 11
66-69 7
70-73
74-77

5. Frequency Distributions
Class boundaries are the numbers used to separate the classes, but without the gaps created by the class limits
Find the center of the gaps and don’t forget about the lower boundary
49.5
53.5
57.5
61.5
65.5
69.5
73.5
77.5
Daily Low Temperature (°F)
Frequency
50-53 1
54-57 3
58-61 5
62-65 11
66-69 7
70-73
74-77

6. Interpret Frequency Distributions
Question: The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of Does the frequency distribution appear to be roughly a normal distribution?
Daily Rainfall (in inches)
Frequency
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11

7. Interpret Frequency Distributions
Answer: What I would do is put the data in numerical ascending order first. Because the frequency is the count and you want to “count” how many data items there are in the range I have them highlighted below (but notice how much easier it would have been if they were sorted)
Daily Rainfall (in inches)
Frequency
 22
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11

8. Interpret Frequency Distributions
Now continue to the
I find 5 values in this range
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11
Daily Rainfall (in inches)
Frequency
 22  5

9. Interpret Frequency Distributions
Then to
I find two values. I also notice all that is left is 1.34 for I put this “one” in the last row
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11
Daily Rainfall (in inches)
Frequency
 22  5  2  0  1

10. Interpret Frequency Distributions
For the second part of the problem:
Does the frequency distribution appear to be roughly a normal distribution?
Answer: Remember graphically this would be a bell curve. If I visually thought about 22 values in the tail end certainly this is not normal. Normal would have more in the middle and less in the ends.
In other words No, the distribution is not symmetric and the frequencies do not start off low.

11. Graphing Frequency Distributions
What if you wanted to actually see the graph of this data in your calculator?
First you need to enter the data in your calculator
Press Stat / Edit and press Enter

12. Graphing Frequency Distributions
You are now looking at a list where you can enter each value
Enter each value from our example and press enter after each value entered
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11

13. Graphing Frequency Distributions
You are now looking at a list where you can enter each value
Enter each value from our example and press enter after each value entered
0.35
0.21
0.51
0.24
1.34
0.19
0.02
0.23
0.18
0.56
0.17
0.11

14. Interpret Frequency Distributions
Daily Rainfall (in inches)
Frequency
 22  5  2  0  1
Next we will set up the Histogram Window
Press Window
We saw from our frequency distribution that our values are between 0 and However, we want to have a little room to right and left
I set my Xmin = -0.5 and Xmax = 1.45

15. Graphing Frequency Distributions
The y values are the vertical direction and in our case the frequencies
These ranged from 0 to 22
Again make a little more room as I set mine to -0.5 and 22.5 for the Ymin and Ymax
Daily Rainfall (in inches)
Frequency
 22  5  2  0  1

16. Graphing Frequency Distributions
Next we will set the Stat Plot
Press 2nd and then Y= to get to the Stat Plot
The first plot should be selected so press ENTER

17. Graphing Frequency Distributions
Turn the Stat Plot On by pressing enter
Down arrow and then to the right to select histogram and press enter
The Xlist: L1 is where the data is located
Remember you typed this in the list 1 column
Press Graph

18. Frequency 22 5 2 0 1 Daily Rainfall (in inches) 0.00-0.19 0.20-0.39
 22  5  2  0  1