Video Solutions to help grade 6 students learn how to construct a frequency histogram and recognize that the number of intervals may affect the shape of a histogram.

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Common Core For Grade 6

Lesson 4 Student Outcomes

• Students construct a frequency histogram.

• Students recognize that the number of intervals may affect the shape of a histogram.

Lesson 4 Summary

A histogram is a graph that represents the number of data values falling in an interval with a bar. The horizontal axis shows the intervals and the vertical axis shows the frequencies (how many data values are in the interval). Each interval should be the same width and the bars should touch each other.

Lesson 4 Classwork

Example 1: Frequency Table with Intervals

The boys and girls basketball teams at Roosevelt Middle School wanted to raise money to help buy new uniforms. They decided to sell hats with the school logo on the front to family members and other interested fans. To obtain the correct hat size, the students had to measure the head circumference (distance around the head) of the adults who wanted to order a hat. The following data represents the head circumferences, in millimeters (mm), of the adults:

The hats come in six sizes: XS, S, M, L, XL, and XXL. Each hat size covers a span of head circumferences. The hat manufacturer gave the students the table below that shows the interval of head circumferences for each hat size. The interval 510 - < 530 represents head circumferences from 510 to 530, not including 530.

Exercises 1–4

1. If someone has a head circumference of 570, what size hat would they need?

2. Complete the tally and frequency columns in the table to determine the number of each size hat the students need to order for the adults who wanted to order a hat.

3. What hat size does the data center around?

4. Describe any patterns that you observe in the frequency column?

One student looked at the tally column and said that it looked somewhat like a bar graph turned on its side. A histogram is a graph that is like a bar graph, except that the horizontal axis is a number line that is marked off in equal intervals. To make a histogram:

• Draw a horizontal line and mark the intervals.

• Draw a vertical line and label it "frequency."

• Mark the frequency axis with a scale that starts at and goes up to something that is greater than the largest frequency in the frequency table.

• For each interval, draw a bar over that interval that has a height equal to the frequency for that interval.

The first two bars of the histogram have been drawn below.

Exercises 5–9

5. Complete the histogram by drawing bars whose heights are the frequencies for those intervals.

6. Based on the histogram, describe the center of the head circumferences.

7. How would the histogram change if you added head circumferences of 551 and 569?

8. Because the 40 head circumference values were given, you could have constructed a dot plot to display the head circumference data. What information is lost when a histogram is used to represent a data distribution instead of a dot plot?

9. Suppose that there had been 200 head circumference measurements in the data set. Explain why you might prefer to summarize this data set using a histogram rather than a dot plot.

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