1. 6-9 Stem-and-Leaf Plots Warm Up Problem of the Day Lesson Presentation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Use the data below to answer each question.
1. What is the median?
2. What is the mode?
3. What is the range? 36
none 33

3. Learn to make and analyze stem-and-leaf plots.

4. A stem-and-leaf plot shows data arranged by place value
A stem-and-leaf plot shows data arranged by place value. You can use a stem-and-leaf plot when you want to display data in an organized way that allows you to see each value.

5. Additional Example 1: Creating Stem-and-Leaf Plots
Use the data in the table to make a stem-and-leaf plot.
Test Scores 75 86 83 91 94 88 84 99 79
Step 1: Group the data by tens digits.
75 79
Step 2: Order the data from least to greatest.

6. Helpful Hint
To write 42 in a stem-and-leaf plot, write each digit in a separate column.
4 2
Stem
Leaf

7. Additional Example 1 Continued
Step 3: List the tens digits of the data in order from least to greatest. Write these in the “stems” column.
75 79
Step 4: For each tens digit, record the ones digits of each data value in order from least to greatest. Write these in the “leaves” column.
Test Scores
Stems
Leaves
Step 5: Title the graph and add a key. 7
5 9 8 9
Key: 7 5 means 75

8. Additional Example 2: Reading Stem-and-Leaf Plots
Find the least value, greatest value, mean, median, mode, and range of the data.
The least stem and least leaf give the least value, 40.
Stems
Leaves 4
The greatest stem and greatest leaf give the greatest value, 94. 5 6 7
0 4 4 8
3 6 7
Use the data values to find the mean (40 + … + 94) ÷ 23 = 64. 9
1 4
Key: 4 0 means 40

9. Additional Example 2 Continued
The median is the middle value in the table, 63.
To find the mode, look for the number that occurs most often in a row of leaves. Then identify its stem. The mode is 63.
Stems
Leaves 4 5 6 7
0 4 4
The range is the difference between the greatest and the least value. 94 – 40 = 54. 8
3 6 7 9
1 4
Key: 4 0 means 40

10. The least stem and least leaf give the least value, 30. Stems Leaves 3
Check It Out: Example 2
Find the least value, greatest value, mean, median, mode, and range of the data.
The least stem and least leaf give the least value, 30.
Stems
Leaves 3
The greatest stem and greatest leaf give the greatest value, 85. 4 5 6
1 2 4
Use the data values to find the mean (30 + … + 85) ÷ 23 = 55. 7
5 6 9 8
1 5
Key: 3 0 means 30

11. Check It Out: Example 2 Continued
The median is the middle value in the table, 56.
To find the mode, look for the number that occurs most often in a row of leaves. Then identify its stem. The mode is 59.
Stems
Leaves 3 4 5 6
1 2 4
The range is the difference between the greatest and the least value. 85 – 30 = 55. 7
5 6 9 8
1 5
Key: 3 0 means 30

12. 1. Make a stem-and-leaf plot of the data.
Lesson Quiz: Part I
1. Make a stem-and-leaf plot of the data.
5 2
Stems
Leaves
Key: 3 | 0 means 30

13. Lesson Quiz: Part II
Find each value using the stem-and-leaf plot.
2. What is the least value?
3. What is the mean?
4. What is the median?
5. What is the mode? 21
34.75 34 34

14. Learn to recognize misleading graphs.
Graphs that cause a reader to misunderstand the information presented may be done intentionally to mislead the reader so that the reader draws an incorrect conclusion from the graph.

15. What could make a graph misleading?
The lower part of the vertical axis is missing.
The vertical axis does not begin at 0.
When comparing two graphs, each graph may be using a different scale.
The intervals are not even.

16. Additional Example 1A: Misleading Bar Graphs
Why is this bar graph misleading?
Because the lower part of the vertical axis is missing, the differences in prices are exaggerated.

17. Additional Example 1B: Misleading Bar Graphs
What might people believe from the misleading graph? 1 2 __ 1 2 __
People might believe that Cars B and C cost 1 to 2
times as much as Car A. In reality, Cars B and C are only a few thousand dollars more than Car A.

18. Why is this bar graph misleading?
Check It Out: Example 1A
Money Raised
600
580
570
Dollars
560
550
540
530
4th graders 5th graders 6th graders
Why is this bar graph misleading?
The vertical axis begins at 530 rather than 0.

19. What might people believe from the misleading graph?
Check It Out: Example 1B
Money Raised
600
580
570
Dollars
560
550
540
530
4th graders 5th graders 6th graders
What might people believe from the misleading graph?
That the 5th graders have raised twice as much money as the 4th graders.

20. Additional Example 2A: Misleading Line Graphs
Why are these graphs misleading?
If you look at the scale for each graph, you will notice that the April graph goes from 54° to 66° and the May graph goes from 68° to 80°.

21. Additional Example 2B: Misleading Line Graphs
What might people believe from these misleading graphs?
People might believe that the temperatures in May were about the same as the temperatures in April. In reality, the temperatures in April were about 15 degrees lower.

22. Additional Example 2C: Misleading Line Graphs
Why is this line graph misleading?
The scale goes from $0 to $80, and then increases by $5.

23. Why are these graphs misleading?
Check It Out: Example 2A
November
September
Temperature (°F)
Temperature (°F)
Week
Week
Why are these graphs misleading?
If you look at the scale for each graph, you will notice that the September Graph goes from 85° to 70° and the November graph goes from 65° to 50°.

24. Check It Out: Example 2B November September Week Week
Temperature (°F)
Temperature (°F)
Week
Week
What might people believe from these misleading graphs?
People might believe that the temperatures in September were about the same as the temperatures in November. In reality, the temperatures in September were about 20 degrees higher.

25. Why is this line graph misleading?
Check It Out: Example 2C
Stock prices
Corp. C
Corp. D 80 70
Price of stock ($) 60 50
Year
Why is this line graph misleading?
The scale goes from $0 to $50, and then increases by $10.

26. Lesson Quiz
1. Why might this line graph be misleading?
2. What might people believe from the graph?
The scale does not start at zero.
Possible answer: that there were hardly any visitors on Monday