1. You will need your calculator today (and every day from now on)

2. Descriptive Statistics
Chapter 2
Descriptive Statistics

3. I. Section 2-1
A. Steps to Constructing Frequency Distributions
1. Determine number of classes (may be given to you)
a. Should be between 5 and 15 classes.
2. Find the Range
a. The Maximum minus the Minimum.
1) Use the TI-84 to sort the data.
a) STAT – Edit – enter numbers into L1
b) STAT – SortA(L1) will put the numbers into ascending order.
c) STAT – SortD(L1) will put the numbers into descending order.
3. Find the Class Width
a. Range divided by the number of classes.
1) Always round UP!!
a) Even if class width comes out to a whole number, go up one.
4. Find the Lower Limits
a. Begin with the minimum value in your data set, and then add the class width to that to get the next Lower Limit.
1) Repeat as many times as needed to get the required number of classes.

4. 5. Find the Upper Limits
a. The Upper Limit of the first class is one less than the Lower Limit of the second class.
1) Add the class width to each Upper Limit until you have the necessary number of classes.
6. Find the Lower Boundaries
a. Subtract one-half unit from each Lower Limit (Do NOT round these!)
7. Find the Upper Boundaries
a. Add one-half unit to each Upper Limit.
8. Find the Midpoints of each class.
a. The means of the Lower and Upper Limits (Do NOT round).
1) Could also use the means of the boundaries for this.
9. Frequency Distribution
a. Place a tally mark in each class for every piece of data that fits there.
b. Add up the tally marks – these are your frequencies for each class.

5. 10. Relative Frequencies
a. Divide the class frequencies by the total number of data points to find the percentage of the total represented by each class.
11. Cumulative Frequencies
a. The total number of tallies for each class, plus all those that came before.
1) The cumulative frequency of the last class must equal the number of data points used.

6. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.72 84 61 76
104 86 92 80 88 98 97 82 67 70 81 89 74 73 85 78 91 83
STAT – Edit –
Enter these 30 numbers into L1 on your calculator
STAT – SortA(L1) – 2nd 1 enters L1 into the parentheses.
STAT – Edit – to see the new list, in order. 61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104

7. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104
Max Value:
Min Value: 61
Range: = 43
Class Width: 43/6 = 7.2
– Round UP to 8! LL UL LB UB
MdPt
Freq.
Rel. Freq.
Cum. Freq.
Minimum Value is the First Lower Limit 61 68
First Upper Limit is one less than 2nd Lower Limit
Add Class Width Down 69 76
Add Class Width Down 77 84 85 92
Check to be sure that the Maximum Value fits in the last class. 93
100
101
108
Since 104 fits between 101 and 108, we are good.
If the Maximum value does NOT fit into the last class, you did something wrong. DO IT AGAIN!! (You PROBABLY forgot to round UP on the class width)

8. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104
Max Value: 104
Min Value: 61
Range:
Class Width: 8 LL UL LB UB
MdPt
Freq.
Rel. Freq.
Cum. Freq.
Subtract one-half unit from lower limits to get lower boundaries 61 68
60.5
68.5
64.5
Find the mean of the limits (or boundaries) to find the midpoint of each class. 69 76
68.5
76.5
72.5 77 84
76.5
84.5
80.5
Add one-half unit to upper limits to get upper boundaries 85 92
84.5
92.5
88.5 93
100
92.5
100.5
96.5
101
108
100.5
108.5
104.5
CHECK – be sure that your class width is actually 8 units!!

9. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104
Max Value: 104
Min Value: 61
Range:
Class Width: 8 LL UL LB UB
MdPt
Freq.
Rel. Freq.
Cum. Freq.
Count how many data points fit in each class and enter that into the Frequency column 61 68
60.5
68.5
64.5 2 69 76
68.5
76.5
72.5 7 77 84
76.5
84.5
80.5 11 85 92
84.5
92.5
88.5 7 93
100
92.5
100.5
96.5 2
Block 7 – frequency of 3rd class
101
108
100.5
108.5
104.5 1

10. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104
Max Value: 104
Min Value: 61
Range:
Class Width: 8 LL UL LB UB
MdPt
Freq.
Rel. Freq.
Cum. Freq.
Relative Frequency is the class frequency divided by the total frequency.
In this case, we have 30 pieces of data, so we divide by 30. 61 68
60.5
68.5
64.5 2
0.067
2/30 69 76
68.5
76.5
72.5 7
0.233
7/30 77 84
76.5
84.5
80.5 11
11/30
0.367 85 92
84.5
92.5
88.5 7
0.233
7/30 93
100
92.5
100.5
96.5 2
2/30
0.067
101
108
100.5
108.5
104.5 1
1/30
0.033
1.00
Relative Frequency column MUST add up to 1!!
If it does NOT, you are wrong. DO IT AGAIN!!

11. EXAMPLE: Use the table of 30 numbers below to fill in a frequency distribution of 6 classes.61 72 76 78 81 82 84 86 89 97 67 73 80 91 70 74 83 85 88 92
104
Max Value: 104
Min Value: 61
Range:
Class Width: 8 LL UL LB UB
MdPt
Freq.
Rel. Freq.
Cum. Freq.
Cumulative Frequency is the Frequency of each class, plus the classes that came before it.
The last class must have a cumulative frequency that matches the number of data points 61 68
60.5
68.5
64.5 2
0.07 2 69 76
68.5
76.5
72.5 7
0.23 9 77 84
76.5
84.5
80.5 11
0.37 20 85 92
84.5
92.5
88.5 7
0.23 27 93
100
92.5
100.5
96.5 2
0.07 29
101
108
100.5
108.5
104.5 1
0.03 30

12. B. Steps to Constructing a Frequency Histogram
1. Label the horizontal axis with the class boundaries.
2. Label the vertical axis with the number of frequencies.
3. Draw a bar graph with bars that touch, using the frequencies from your frequency distribution.

13. C. Steps to Constructing a Relative Frequency Histogram
1. Label the horizontal axis with the class boundaries.
2. Label the vertical axis with the frequency percentages.
3. Draw a bar graph with bars that touch, using the relative frequencies from your frequency distribution.

14. D. Steps to Constructing an Ogive
1. Label the horizontal axis with the midpoints of each class.
2. Label the vertical axis with the total number of data points.
3. Place a dot at each midpoint that corresponds to that class’s cumulative frequency.
a. This chart will always end at the total number of data points.

15. Assignments:
Classwork: Pages #1-8 All, Evens
Homework: Pages #29-41 Odds