1. Teacher
Intro Stats
Lesson 2.1 B
Objective: SSBAT construct an expanded frequency distribution chart.
Standards: S2.5B

2. Expanded Frequency Distribution
Adds 3 more columns to the frequency distribution from yesterday - Midpoints, Relative Frequency, and Cumulative Frequency
These 3 columns will help to provide a better understanding of the data

3. The Average of the lower and upper limit of each class
Midpoint of a Class
The Average of the lower and upper limit of each class
Midpoint of Class = lower + upper 2
You will use this formula for each row of the frequency distribution

4. Relative Frequency
The portion or percentage of the data that falls in that class
Divide the Frequency of that Class by the number of data entries
Relative Frequency = 𝐂𝐥𝐚𝐬𝐬 𝐅𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲 # 𝐨𝐟 𝐃𝐚𝐭𝐚 𝐄𝐧𝐭𝐫𝐢𝐞𝐬

5. Cumulative Frequency
The sum of the Frequency for that class and all previous class frequencies

7. Find the Midpoints, Relative Frequency and Cumulative Frequency for the following.
Class
Tally
Frequency (f)
Midpoint
Relative Frequency
Cumulative
Frequency
2 – 7
lllllll 7
8 – 13
lllllllllll 11
14 – 19
20 – 25
26 – 31
llll 4
Σf = 36

8. Problem 1 continued.
Midpoints
= 4.5
= 10.5
= 16.5
= 22.5
 = 28.5

9. Class Tally Frequency (f) Midpoint Relative Frequency Cumulative
Problem 1 continued.
Class
Tally
Frequency (f)
Midpoint
Relative Frequency
Cumulative
Frequency
2 – 7
lllllll 7
4.5
8 – 13
lllllllllll 11
10.5
14 – 19
16.5
20 – 25
22.5
26 – 31
llll 4
28.5
Σf = 36

10. .11 .19 .31 Class Tally Frequency (f) Midpoint Relative Frequency
Problem 1 continued.
Relative Frequency = Class Frequency # of Data Entries
Class
Tally
Frequency (f)
Midpoint
Relative Frequency
Cumulative
Frequency
2 – 7
lllllll 7
4.5
8 – 13
lllllllllll 11
10.5
14 – 19
16.5
20 – 25
22.5
26 – 31
llll 4
28.5
Σf = 36
.19
.31
.11

11. 32 36 7 18 25 Class Tally Frequency (f) Midpoint Relative Frequency
Problem 1 continued.
Cumulative Frequency
The sum of the Frequency for that class and all previous classes
Class
Tally
Frequency (f)
Midpoint
Relative Frequency
Cumulative
Frequency
2 – 7
lllllll 7
4.5
.19
8 – 13
lllllllllll 11
10.5
.31
14 – 19
16.5
20 – 25
22.5
26 – 31
llll 4
28.5
.11
Σf = 36 7 18 25 32 36

13. 2. Find the Midpoints, Relative Frequency and
2. Find the Midpoints, Relative Frequency and Cumulative Frequency for the following.
Class
Frequency
Midpoint
Relative Frequency
Cumulative Frequency
7 – 18 6
19 – 30 10
31 – 42 13
43 – 54 8
55 – 66 5
67 – 78
79 – 90 2
∑f = 50
12.5
24.5
36.5
48.5
60.5
72.5
84.5

14. Class Frequency Midpoint Relative Frequency Cumulative Frequency
2. Relative Frequency  Frequency ÷ Total #
Class
Frequency
Midpoint
Relative Frequency
Cumulative Frequency
7 – 18 6
19 – 30 10
31 – 42 13
43 – 54 8
55 – 66 5
67 – 78
79 – 90 2
∑f = 50
12.5
24.5
36.5
48.5
60.5
72.5
84.5
.12 .2
.26
.16 .1
.04

15. Class Frequency Midpoint Relative Frequency Cumulative Frequency
2. Cumulative Frequency  Class Frequency + Above Frequencies
Class
Frequency
Midpoint
Relative Frequency
Cumulative Frequency
7 – 18 6
19 – 30 10
31 – 42 13
43 – 54 8
55 – 66 5
67 – 78
79 – 90 2
∑f = 50
12.5
24.5
36.5
48.5
60.5
72.5
84.5
.12 .2
.26
.16 .1
.04 6 16 29 37 42 48 50

16.  Example Three is worksheet 2.1 B

17. 4. Find the Midpoints, Relative Frequency and
4. Find the Midpoints, Relative Frequency and Cumulative Frequency for the following.
Class
Frequency
Midpoint
Relative Frequency
Cumulative Frequency
1 – 5 5
6 – 10 8
11 – 15 4
16 – 20 7
21 – 25 6
26 – 30
∑f = 34

18. 5 13 17 24 30 34 4. Answers to #3 Class Frequency Midpoint
Relative Frequency
Cumulative Frequency
1 – 5 5 3 
.15  5 
6 – 10 8  8
 .24
 13
11 – 15 4
 .12
 17
16 – 20 7
18 
 .21
 24
21 – 25 6
23 
 .18
 30
26 – 30
28 
 34
∑f = 34

19. Homework
Worksheet 2.1 B