1. Frequency Tables Histograms
Reporting Frequency
Frequency Tables
Histograms

2. Frequency Tables and Histograms Review:
Reporting Frequency:
Frequency Tables and Histograms
Review:
Stem-and-Leaf Plots, and Line Plots
Warm Up
Problem of the Day
Lesson Presentation
Course 2

3. Warm Up Almost 14 years Jason deposits $200 in an account that earns
3.6% simple interest. How long until the total
amount $300.
Almost 14 years
Course 2

4. Problem of the Day
Books A, B, C, and D are on the bookshelf. A is between C and B. B is between A and D. D is not on the right. What is the order of the books from right to left?
D, B, A, C
Course 2

5. Learn to organize and interpret data in frequency tables and histograms.
Review organizing data in stem-and-leaf plots, and line plots.

6. Vocabulary frequency table cumulative frequency histogram
stem-and-leaf plot
line plot

7. Things we know:
Stem-and-Leaf Plot
A stem-and-leaf plot can be used to show how often data values occur and how they are distributed. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents left-hand digits.
Stems Leaves
Key: 2|7 means 27

8. Example 1: Organizing and Interpreting Data in a Stem-and-Leaf Plot
The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years.
33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17
Step 1: Order the data from least to greatest. Since the data values range from 12 to 40, use tens digits for the stems and ones digits for the leaves.

9. Example 1 Continued Stems Leaves 1 2 3 4
The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years.
33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17
Step 2: List the stems from least to greatest on the plot.
Stems Leaves
The stems are the tens digits. 1 2 3 4

10. Example 1 Continued Stems Leaves 2 5 5 7 7 8 1 2 3 4 1 2 3 3 9 3 3
The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years.
33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17
Step 3: List the leaves for each stem from least to greatest.
Stems Leaves
The stems are the tens digits.
The leaves are the ones digits. 2 5 5 7 7 8 1 2 3 4 1 2 3 3 9 3 3

11. Number of Years Coached
Example 1 Continued
Step 4: Add a key and a title.
Stems Leaves 1 2 3 4 5 7 8 9
Number of Years Coached
The stems are the tens digits.
The leaves are the ones digits.
Key: 2 | 1 means 21.
11 coaches coached fewer than 25 years.

12. Your Turn: Example 2 Step 1:
The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times.
55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41
Step 1:
Order the data from least to greatest. Since the data values range from 23 to 68, use tens digits for the stems and ones digits for the leaves.

13. Your Turn: Example 2 Continued
The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times.
55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41
Step 2: List the stems from least to greatest on the plot.
Stems Leaves
The stems are the tens digits. 2 3 4 5 6

14. Your Turn: Example 2 Continued
The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times.
55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41
Step 3: List the leaves for each stem from least to greatest.
Stems Leaves 2 3 4 5 6
The stems are the tens digits.
The leaves are the ones digits. 3 7 8 9 3 5 7 8 1 1 3 5 5 1 2 8

15. Number of times a Soccer Player can bounce the ball on their knee
Your Turn: Example 2 Continued
Step 4: Add a key and a title.
Number of times a Soccer Player can bounce the ball on their knee
Stems Leaves 2 3 4 5 6 7 8 9 1
The stems are the tens digits.
The leaves are the ones digits.
Key: 4 | 0 means 40.
12 soccer players can bounce the ball on their knee more than 36 times.

16. Example 3: Organizing and Interpreting Data in a Line Plot
Make a line plot of the data. How many hours per day did Morgan babysit most often?
Number of Babysitting Hours in July M T W Th F S Su
Wk 1 6 4 5 8 2
Wk 2 7
Wk 3 1
Wk 4 3

17. DAY 2 Period 3
Example 3 Continued
Make a line plot of the data. How many hours per day did Morgan babysit most often?
Step 1: The data values range from 0 to 8. Draw a number line that includes this range.

18. Example 3 Continued
Make a line plot of the data. How many hours per day did Morgan babysit most often?
Step 2: Put an X above the number on the number line that corresponds to the number of babysitting hours in July.
XXXXXX
XXXX
XXXX
XXX
XXX
XXX XX XX X
The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.

19. Your Turn: Example 4
Make a line plot of the data. How many slices of pizza did most people eat?
Number of Slices eaten per Person 2 4 1 5 3 6

20. Example 4 Continued
Make a line plot of the data. How many slices of pizza did most people eat?
Step 1: The data values range from 0 to 6. Draw a number line that includes this range.

21. Example 4 Continued
Make a line plot of the data. How many slices of pizza did most people eat?
Step 2: Put an X above the number on the number line that corresponds to the number slices of pizza eaten per person.
XXXXXX
XXXX
XXX
XXX
XXX X X
The greatest number of X’s appear above the number 2. This means that most people ate 2 slices of pizza.

22. A frequency table is best used to keep track of and organize data!
We can even use them to help keep up with data as we are conducting our surveys!

23. A frequency table is a way to organize data into categories or groups
A frequency table is a way to organize data into categories or groups. It lists each item in a data set with the number of times it occurs.
By including a cumulative frequency column in your table, you can keep a running total of the frequencies in each category.

24. # of Cats in Homes A frequency table contains 3 columns. # of Cats
Tally
Frequency
|||| 5 1
||||| | 6 2
||| 3
3 or more |

25. Example 5: Organizing and Interpreting Data in a Frequency Table
DAY 2 Period 2, 1
Example 5: Organizing and Interpreting Data in a Frequency Table
The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees?
69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2
February Temperatures in 20 Cities
Average Highs
Frequency
Cumulative Frequency
Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals.
0–19
20–39
40–59
60–79

26. Example 5 Continued
The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees?
69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2
February Temperatures in 20 Cities
Average Highs
Frequency
Cumulative Frequency
Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column.
0–19 7
20–39 5
40–59 5
60–79 3

27. Example 5 Continued 0–19 20–39 40–59 60–79 7 5 3 7 12 17 20
The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees?
69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2
February Temperatures in 20 Cities
Average Highs
Frequency
Cumulative Frequency
0–19
20–39
40–59
60–79 7 5 3
Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 7 12 17 20
17 cities had average high temperature below 59 degrees.

28. Your Turn: Example 6 60–69 70–79 80–89 90–99
The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below?
85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96
English Exam Grades
Grades
Frequency
Cumulative Frequency
Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals.
60–69
70–79
80–89
90–99

29. Your Turn: Example 6 Continued
The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below?
85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96
English Exam Grades
Grades
Frequency
Cumulative Frequency
60–69
70–79
80–89
90–99
Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. 4 4 6 6

30. Your Turn: Example 6 Continued
The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below?
85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96
English Exam Grades
Grades
Frequency
Cumulative Frequency
60–69
70–79
80–89
90–99 4 6
Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 4 8 14 20
8 students received grades of 79 or below.

31. What is a Histogram?
Period 3 Day 3
A histogram is a bar graph with no spaces between the bars. The height of each bar shows the frequency of data within that interval. The intervals of a histogram are of equal size and do not overlap.

32. Histogram
Example 7
Class Test Scores
Frequency
Test Scores

33. Histograms
Example 8
95 flashlights are tested until they fail. The table gives the times taken ( hours ) until failure.
Time to failure (hours)
0-19
20-29
30-39
40-44
45-49
50-59
60-89
Number of components 5 8 16 22 18 10
Find 2 or more things wrong with the histogram which represents the data in the table.

34. Example 8 Continue 0-19 20-29 30-39 40-44 45-49 50-59 60-89 5 8 16 22
Histograms
Example 8 Continue
Answer:
Time to failure (hours)
0-19
20-29
30-39
40-44
45-49
50-59
60-89
Number of components 5 8 16 22 18 10
Time taken for 95 components to fail
There is no title.
There are no units on the x-axis.
Time to failure (Hours)

35. Histogram – a bar graph that gives the frequency of each
value.
In a histogram, the horizontal axis is like a number line
divided into equal widths.
Each width represents a data value or range of data values.
The height of each bar indicates the frequency of
that data value or range of data values.

36. Example 9

37. *Ex 10. The given data shows the # of people in 24 vehicles
that passed a designated checkpoint.
1, 4, 1, 2, 2, 1, 3, 1, 3, 2, 2, 6,
4, 2, 1, 1, 2, 4, 3, 1, 2, 4, 2, 3.
a.) Make a frequency table for these data.
b.) Make a histogram from the frequency table. #
Frequency 1 2 3 4 5 6

38. *Ex11. Use the relative frequencies given to estimate
the probability that a randomly selected customer will
rent a canoe for 5 or more hours.
Question: What % rented a canoe for 5, 6, 7, and 8 hours?
Hours
Frequency
Relative Frequency 1 3
3/30 = 0.10 = 10% 2 10 7 4 5 6 8
Total 30

39. Histogram Histograms are used to show the frequency of data.
Very similar to bar graphs, but use intervals on the X axis.
Bars do touch.
Histograms have a title.
Histograms have two axes which are labeled.

40. NOW LET US GET THAT PROJECT DONE
Frequency Tables
Histograms