4-22-13 Histograms

EQ: What conclusions can be drawn from a histogram? What can a histogram tell you about the spread of a data set?

DWP - Mr. Adams had 24 guests at his house for a party. Each guest brought one item.• One-third of the guests brought drinks.• One-fourth of the guests brought a dessert.• The rest of the guests brought chips.How many guests brought chips?

BOP

2

132

4

1162

DWP - Mr. Adams had 24 guests at his house for a party. Each guest brought one item.• One-third of the guests brought drinks.• One-fourth of the guests brought a dessert.• The rest of the guests brought chips.How many guests brought chips?

12

5

12

7

12

1212

7

12

3

12

4

4

1

3

1

Concept/Vocabulary Word Definition

Cluster a group of things or persons close together

Distribution The arrangement of values in a data set

Frequency Table A list of items or intervals that shows the number of times, or frequency, with which they occur.

Gap a break or opening

HistogramA display that shows the distribution of numeric data. The range of data values, divided into intervals, is displayed on the horizontal axis. The vertical axis shows frequency.

intervalis a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set

Peak being at the point of maximum frequency, intensity, use, etc.

Hundreds of different languages are spoken around the world. The graph shows the numbers of native speakers of four languages.

A bar graph can be used to display and compare data. The scale of a bar graph should include all the data values and be easily divided into equal intervals.

A histogram is a bar graph that shows the frequency of data within equal intervals. There is no space between the bars in a histogram.Follow these steps to make a histogram:

Step 1: Make a frequency table of the data. Be sure to use equal intervals.

Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

Step 4: Label the axes and give the graph a title.

PUT THESE STEPS IN YOUR STUDY GUIDE!

The table below shows the number of hours students watch TV in one week. Make a histogram of the data.

Example 3: Making a Histogram

Step 1: Make a frequency table of the data. Be sure to use equal intervals.

Course 2

1-4 Bar Graphs and Histograms

6 ///7 //// ////8 ///9 ////

1 //2 ////3 //// ////4 //// /5 //// ///

Number of Hours of TV

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

Example 3 Continued

Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

Course 2

1-4 Bar Graphs and Histograms

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

Example 3 Continued

Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

Course 2

1-4 Bar Graphs and Histograms

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

Additional Example 3 Continued

Step 4: Label the axes and give the graph a title.

Course 2

1-4 Bar Graphs and Histograms

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

1–3 4–6 7–9

Hours of Television Watched

Freq

uenc

y

Hours

Follow the steps to create a histogram.

Mrs. Pittman gave her class a history test. The class of 16 students had the following scores:

75, 80, 65, 80, 95, 85, 65, 80, 90, 80, 70, 85, 90, 70, 85, 70

Construct A Histogram

PUT FINAL GRAPH IN YOUR STUDY GUIDE!

Step 1 - Make a Frequency Table

Grade range

Frequency

60-6970-7980-8990-99

Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.

Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

Step 4: Label the axes and give the graph a title.

The graph below shows the results of a survey of 390 families.

How many of the families in the survey have more than three children?A. 120 B. 130 C. 140 D. 260

The graph below shows the results of a survey of 390 families.

B. 130

CC Investigation Grade Six Page 53 #13-15 Holt Course 2 Lesson 1-4 Practice

CC Investigations 1. Basketball TournamentThe table shows the winning scores in the first round of the basketball tournament.

90 69 70 89 62 97 64 68

79 67 77 66 65 89 99 82

100 81 78 53 80 62 86 77

73 77 69 72 52 68 80 73

On a separate sheet of paper, construct frequency tables and histograms for the following problems. Turn in for a class work grade.

1.What are the greatest and least winning scores?2.Divide the range of the data into equal intervals that will be represented by bars on the histogram. Give the range for each interval.3.Explain why you chose that number of intervals.4.Make a table to show the frequency of scores in each interval.5. Make a histogram of the data. Draw a bar for each interval to represent the frequency. 6. Summarize what the histogram show about the data.

2. Ages of mall shoppers

23 33 21 18 17 45 40 2312 31 27 27 29 24 12 4019 18 25 17 36 40 38 20

3. Class grades on a history exam

97 84 93 76 87 100 92 9070 85 83 99 90 89 84 91100 96 76 74 73 87 80 93

4. Weights of pumpkins in lbs.

5 16 23 8 7 9 12 1520 15 7 18 6 6 21 168 11 12 16 10 20 23 914 24 17 7 6 18 9 10

Answers for basketball tournament1. 100; 512. 51-60, 61-70, 71-80, 81-90, 91-1003. Five intervals divides the data into enough groups without making a histogram that is too large.4.

Interval Frequency 51-60 261-70 1171-80 1081-90 6

91-100 3

What are the SIMILARITIESandDIFFERENCESbetween bargraphs andhistograms?

EXIT TICKET

EXIT TICKET: What are the SIMILARITIES and DIFFERENCES between bar graphs and histograms?

Homework:

Correct all problems on geometry handouts completed in class last week. It was checked on Friday for a class work grade.

Make all corrections on a separate sheet of paper. Staple corrections to the top of the original papers.All corrections are due on Wednesday.

Did you note this information in your chart?

The difference is that a bar graph represents individual pieces of data where the histogram represents intervals of data.

The bar graph usually has spaces between the bars where the histogram has the bars adjacent to each other.

Both should have a title, the labels for the axes, and scale for the axes.

Complete workbook page 4