Download Warm-Up

Lesson 4.4
Core Focus on
Ratios, Rates & Statistics
Histograms
Warm-Up
Vicente asked some of his friends
about the number of hours they
spent doing chores each week.
Use the dot plot to answer the
following questions.
1. How many friends did Vicente survey?
10
2. What was the range of the data?
6
3. Find the mean, median and mode of the data.
Mean = 2.4; Median = 2; Mode = 2
Lesson 4.4
Histograms
Make, read and interpret histograms.
Vocabulary
Histogram
A bar graph in which data values are organized into equal intervals.
Histograms display data in the form of numbers whereas bar graphs
display data in categories.
Good to Know!
Each interval on a histogram includes
the number on the left-hand side of an
interval up to the number on the righthand side.
Frequency Table
A table which shows a tally of how many
times a value occurred in each interval.
Example 1
Use the histogram to answer each
question.
a. How many students had
2 or 3 pets?
Ten students have 2 or 3 pets. Look at the height (number of
students) of the bar that is between 2 and 4.
Example 1 Continued…
Use the histogram to answer each
question.
b. How many students had at least
8 pets?
There are 3 students who have at least 8 pets. Adding the
bars to the right of 8 on the horizontal axis (1 + 2) totals 3.
Example 1 Continued…
Use the histogram to answer each
question.
c. The interval between 6 – 8 is
empty. What does that mean?
This means that there are 0 students who had
exactly 6 or 7 pets.
Example 1 Continued…
Use the histogram to answer each
question.
d. How many students are in
Ms. Sanchez’ class?
Add the heights of all the
bars together.
13 + 10 + 5 + 0 + 1 + 2
= 31 students
This sum represents the number of students in the class.
Making A Histogram
1. Identify the minimum and maximum numbers in the
data set.
2. Choose an appropriate interval width. Histograms
usually have 4 to 12 intervals.
3. Make a frequency table. Tally the number of times a
value occurs in each interval.
4. Place the intervals from the frequency table along
the horizontal axis of the graph.
5. Create bars for each interval. The height of each bar
should equal the number of tally marks in each
interval in the frequency table.
Good to Know!
Any interval width works for histograms. However, it is ideal to
have between 4 and 12 intervals to best display the distribution of
data in a histogram.
Too few intervals in a
histogram will not show
the distribution in the
graph well.
Too many bars will
spread the data out so
the bars will have very
little height.
Example 2
Make a histogram for students’ pulse rates (in beats per minute)
listed below.
64, 76, 60, 70, 68, 70, 88, 62, 54, 68, 70, 72, 60, 92, 64, 76, 70, 68, 62, 72
Identify the minimum and maximum values.
Minimum = 54
Maximum = 92
The frequency table must start low enough to
include 54 and must go high enough to include 92.
The overall range of the data is 92 – 54 or 38.
Determine an appropriate interval width.
An interval width of 5 will create about 8 bars.
38 ÷ 8 ≈ 5
Example 2 Continued…
Make a histogram for students’ pulse rates (in beats per minute)
listed below.
64, 76, 60, 70, 68, 70, 88, 62, 54, 68, 70, 72, 60, 92, 64, 76, 70, 68, 62, 72
Complete the frequency table for the data.
When a number in the data
set lies on the border of
two intervals, put it in the
uppermost interval.
Example 2 Continued…
Make a histogram for students’ pulse rates (in beats per minute)
listed below.
64, 76, 60, 70, 68, 70, 88, 62, 54, 68, 70, 72, 60, 92, 64, 76, 70, 68, 62, 72
Use the information collected in the frequency table to draw the
histogram.
There were 20
students’ pulse
rates. The heights of
the bars sum to 20.
Communication Prompt
Give an example of real-world data that could be
displayed in a bar graph. Give an example of realworld data that could be displayed in a histogram.
Exit Problems
Use the histogram to answer the following questions.
1. What is the interval width?
6
2. Which interval has the most values?
12 – 18
3. How many values are in the data set?
13
4. How many values are 18 or higher?
5
5. In which interval would the number 12 be included?
12 – 18