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Describing a Distribution Displayed in a Histogram


Video Solutions to help grade 6 students learn how to construct a relative frequency histogram.

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Common Core For Grade 6

New York State Common Core Math Module 6, Grade 6, Lesson 5

Lesson 5 Student Outcomes

• Students construct a relative frequency histogram.
• Students recognize that the shape of a histogram does not change when relative frequency is used compared to when frequency is used to construct the histogram.

Lesson 5 Summary

A relative frequency histogram uses the same data as a frequency histogram but compares the frequencies for each interval frequency to the total number of items.
The only difference between a frequency histogram and a relative frequency histogram is that the vertical axis uses relative frequency instead of frequency. The shapes of the histograms are the same as long as the intervals are the same.

Lesson 5 Classwork

Example 1: Relative Frequency Table
In Lesson 4, we investigated the head circumferences that the boys and girls basketball teams collected. Below is the frequency table of the head circumferences that they measured.
Isabel, one of the basketball players, indicated that most of the hats were small, medium, or large. To decide if Isabel was correct, the players added a relative frequency column to the table. Relative frequency is the value of the frequency in an interval divided by the total number of data values.

Exercises 1–4
1. Complete the relative frequency column in the table below.
2. What is the total of the relative frequency column?
3. Which interval has the greatest relative frequency? What is the value?
4. What percent of the head circumferences is between and ? Show how you determined the answer.

Example 2: Relative Frequency Histogram
The players decided to construct a histogram using the relative frequencies instead of the frequencies. They noticed that the relative frequencies in the table ranged from close to 0 to about 0.40. They drew a number line and marked off the intervals on that line. Then, they drew the vertical line and labeled it relative frequency. They added a scale to this line by starting at 0 and counting by 0.05 until they reached 0.40.
They completed the histogram by drawing the bars so the height of each bar matched the relative frequency for that interval. Here is the completed relative frequency histogram:

Exercises 5–6
5. Answer the following questions.
a. Describe the shape of the relative frequency histogram of head circumferences from Example 2.
b. How does the shape of this histogram compare with the frequency histogram you drew in Exercise 5 of Lesson 4?
c. Isabel said that most of the hats that needed to be ordered were small, medium, and large. Was she right?
What percent of the hats to be ordered is small, medium, or large?

6. Here is the frequency table of the seating capacity of arenas for the NBA basketball teams.
a. What is the total number of NBA arenas?
b. Complete the relative frequency column. Round to the nearest thousandth.
c. Construct a relative frequency histogram. Round to the nearest thousandth.
d. Describe the shape of the relative frequency histogram.
e. What percent of the arenas has a seating capacity between 18,5000 and 19,999 seats?
f. How does this relative frequency histogram compare to the frequency histogram that you drew in problem 2 of the Problem Set in Lesson 4?


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