Unit 8, Lesson 8
Describing Distributions on Histograms
Grade 6
8.1
Warm-up
Which three go together? Why do they go together?
Histogram A, horizontal axis 45 to 155 by tens. Beginning at 75 up to but not including 85, height of bar at each interval is 7, 29, 30, 25, 3.
Histogram B, horizontal axis 45 to 155 by tens. Beginning at 55 up to but not including 65, height of bar at each interval is 7, 29, 30, 25, 3.
Histogram C, horizontal axis 45 to 155 by tens. Beginning at 55 up to but not inluding 65, height of bar at each interval is 1, 6, 15, 17, 26, 16, 6, 4, 0, 2.
Histogram D, horizontal axis 45 to 155 by tens. Beginning 75 up to but not including 85, height of bar at each interval is 4, 19, 25, 12, 7.
8.3
Activity
Your teacher will provide you with some data that your class collected the other day.
- Use the data to draw a histogram that shows your class’s travel times.
- Describe the distribution of travel times. Comment on the center and spread of the data, as well as the shape and features.
- Use the data on methods of travel to draw a bar graph. Include labels for the horizontal axis.
- Describe what you learned about your class’s methods of transportation to school. Comment on any patterns you noticed.
-
Compare the histogram and the bar graph that you drew. How are they the same? How are they different?
Student Lesson Summary
We can describe the shape and features of the distribution shown on a histogram. Here are two distributions with very different shapes and features.
A histograms labeled “A” where the horizontal axis has the numbers 10 through 30, in increments of 2, indicated and on the vertical axis, the numbers 0 through 6 are indicated. The data represented by the bars on histogram are: 10 up to 12, 0; 12 up to 14, 1; 14 up to 16, 2, 16 up to 18, 4; 18 up to 20, 5; 20 up to 22, 6; 22 up to 24, 4, 24 up to 26, 3; 26 up to 28, 2; 28 up to 30, 1.
A histogram, labeled “B” where the horizontal axis has the numbers 10 through 30, in increments of 2, indicated and on the vertical axis, the numbers 0 through 6 are indicated. The data represented by the bars on histogram are: 10 up to 12, 5; 12 up to 14, 3; 14 up to 16, 2; 16 up to 18, 2; 18 up to 20, 1; 20 up to 22, 0; 22 up to 24, 1; 24 up to 26, 3; 26 up to 28, 2; 28 up to 30, 1.
- Histogram A is very symmetrical and has a peak near 21. Histogram B is not symmetrical and has two peaks, one near 11 and one near 25.
- Histogram B has two clusters. A cluster forms when many data points are near a particular value (or a neighborhood of values) on a number line.
- Histogram B also has a gap between the clusters from 20 and 22. A gap shows a location with no data values.
Here is a bar graph showing the breeds of 30 dogs and a histogram for their weights.
A bar graph has three categories on the horizontal axis labeled "pugs," "beagles," and "German shepherds." The vertical axis has the numbers 0 through 12, in increments of 3, indicated. The bar labeled “pugs” has a height of 9. The bar labeled “beagles” has a height of 9” and the bar labeled “German shepherds” has a height of 12.
A histogram has a horizontal axis labeled “dog weights in kilograms.” The vertical axis has the numbers 0 through 10, in increments of 2, indicated. The data represented by the bars are as follows: 10 up to 15 kilograms, 5; 15 up to 20 kilograms, 7; 20 up to 25 kilograms, 10; 25 up to 30 kilograms, 3; 30 up to 35 kilograms, 5.
Bar graphs and histograms may look alike, but they have different uses.
- Bar graphs represent categorical data. Histograms represent numerical data.
- Bar graphs have spaces between the bars. Histograms show a space between bars only when no data values are in an interval.
- Bars in a bar graph can be in any order. Histograms must be in numerical order.
- In a bar graph, the number of bars depends on the number of categories. In a histogram, we choose how many bars to use.
None