1. Collecting, Organizing and Interpreting Data

2. There are many reasons people collect data in the real world.
Businesses may want to know the opinions of their workers.
Companies may want to know how people spend their money.
Students might want to know which hobbies or sports other 4th graders enjoy.

3. In order to find out this type of information, a survey is often taken.
Cafeteria workers may take a survey to find out which foods are preferred.
Advertisers may survey buyers to see what they like most about the product.
States and communities may take surveys to find out which candidate is most popular among voters or where tax dollars are most needed.

4. When you collect data, you will need a way to keep track of the information you gather.
That’s where stem-and-leaf plots, frequency tables or dot plots can help.

5. Let’s look at a stem-and-leaf plot first.
This data is organized into a stem-and-leaf plot here.
Age of Texas Rangers’ Outfielders
2 3
Key: 2|1 means 21 years old
Player
Age
S. Choo 34
D. DeShields 24
J. Hamilton 35
N. Mazara 21
R. Rua 26
J. Ruggiano

6. Yes, it is a bit tricky at first but you’ll catch on.
Looks a little tricky?
Yes, it is a bit tricky at first but you’ll catch on.
A stem-and-leaf plot is a quick way of jotting down numbers with at least two digits.

7. Think about how several leaves may be attached to the same stem.
This idea will help you understand how to create your own stem-and-leaf plots.

8. 23 1 4 6 4 4 5 Player Age S. Choo 34 D. DeShields 24 J. Hamilton 35
N. Mazara 21
R. Rua 26
J. Ruggiano
In this example, the stems are the numbers in the tens place.
Age of Texas Rangers’ Outfielders 23
Key: 2|1 means 21 years old

9. 23 1 4 6 4 4 5 Player Age S. Choo 34 D. DeShields 24 J. Hamilton 35
N. Mazara 21
R. Rua 26
J. Ruggiano
There are 3 values with twenties and 3 values with thirties. But you only need to write the stem of 2 and the stem of 3 once.
Age of Texas Rangers’ Outfielders 23
Key: 2|1 means 21 years old

10. 23 1 4 6 4 4 5 Player Age S. Choo 34 D. DeShields 24 J. Hamilton 35
N. Mazara 21
R. Rua 26
J. Ruggiano
After all the stems are recorded, there is a vertical line drawn to separate the stems from the leaves.
Age of Texas Rangers’ Outfielders 23
Key: 2|1 means 21 years old

11. 23 1 4 6 4 4 5 Player Age S. Choo 34 D. DeShields 24 J. Hamilton 35
N. Mazara 21
R. Rua 26
J. Ruggiano
Now it is time to add the leaves. These are the numbers in the ones place.
Unlike the stems, each number in the ones place must be recorded .
Age of Texas Rangers’ Outfielders 23
Key: 2|1 means 21 years old

12. Turn to your partner or table team and discuss what you just learned about stem-and-leaf plots and what questions you still have.

13. Here’s another example and then it will be your turn to try it.

14. Mrs. Baker wrote all the test scores on the board.
Test Grades:
Then she organized the data by writing the scores in order from least to greatest.

15. Now, it is easier to find the least and greatest values.
Test Grades:
She will use the digits in the tens place and hundreds place as the stems.

16. The stems are 6, 7, 8, 9, and 10. Test Grades:
She will use the digits in the tens place and hundreds place as the stems.

17. She will show each piece of the data by writing the stems first, drawing a vertical line, and then writing the leaves. 6 7 8 9 10 2
2 6
0 0
Remember, the digits in the tens place are the stems and the digits in the ones place are the leaves.

18. Let’s zoom in and take a closer look.6 7 8 9 10 2
2 6
0 0
Key: 6|2 means a grade of 62.
Now, let’s write a key that explains how to read the stems and leaves.

19. Let’s title the plot and discuss the data.
Friday’s Test Grades 6 7 8 9 10 2
2 6
0 0
Key: 6|2 means a grade of 62.

20. Two students made an 84 so the numbers must be repeated.
Friday’s Test Grades 6 7 8 9 10 2
2 6
0 0
Key: 6|2 means a grade of 62.
Be sure to include the zeros to represent the two scores of 100.

21. Let’s Review . . .
The fourth grade boys recorded their height in inches.
Rewrite the data from least to greatest.
Choose the stems. In this case, it will be 3, 4, and 5. 3 4 5
8 9
0 1
Don’t forget to write down every digit in the ones place for the leaves.

22. Let’s Practice . . .
George Washington 67
John Adams 90
Thomas Jefferson 83
James Madison 85
James Monroe 73
John Q. Adams 80
Andrew Jackson 78
Martin Van Buren 79
William Harrison 68
John Tyler 71
James K. Polk 53
Zachary Taylor 65
The first 12 presidents and the number of years they lived are recorded in the chart to the right.
Make a stem-and-leaf plot to organize the life span of our first 12 presidents.

23. Compare Your Answer
Life Span of 12 Presidents
5 3
Key: 5|3 means 53 years
The stem-and-leaf plot makes it easy to see at a glance that more Presidents died in their 70s than in their 50s or 90s.

24. You are off to a great start understanding how to interpret and create a stem-and-leaf plot.
However, data may contain larger numbers or even fractions and decimals.
Just think of your leaves as the digit to the right and the stems as the digit or digits to the left.

25. The key is an important part of interpreting the data.
These are the 4th grade girls’ shoe sizes.
5, 5, 5 , 6, 6, 6 , 6 , 7, 7, 7
Here is the same data in a stem-and-leaf plot.
It is important to use zeros to represent the whole sizes of 5, 6, and 7.
The key is an important part of interpreting the data.
Girls’ Shoe Sizes
Key: 5| means 5

26. Which is more reasonable?
Notice why the key is so important.
In this
stem-and-leaf plot, the greatest value would be 3.9 miles and the least value would be 1.4 miles using this key.
In this stem-and-leaf plot, the greatest value would be 39 miles and the least value would be 14 miles using this key.
Miles Ran Last Week
Key: 1| 4 means 1.4
Key: 1| 4 means 14
Which is more reasonable?

27. Let’s Practice . . .
Rusty created the table below to show the hours he spent watching T.V. last week.
Sunday 2
Monday
1.5
Tuesday
0.5
Wednesday
Thursday 1
Friday
Saturday
2.5
Use Rusty’s data to create a stem-and-leaf plot. Don’t forget to include a title and a key.

28. Hours Rusty Spent Watching T.V.
Compare Your Answer
Hours Rusty Spent Watching T.V.
0 5
Key: 0|5 means 0.5 hours
Sunday 2
Monday
1.5
Tuesday
0.5
Wednesday
Thursday 1
Friday
Saturday
2.5

29. Hours Rusty Spent Watching T.V.
Here’s Another Possibility
If Rusty recorded 2.25 or 1.75 miles the result would look like this.
Hours Rusty Spent Watching T.V.
0 50
Key: 2|25 means 2.25 hours
Sunday
2.25
Monday
1.5
Tuesday
0.5
Wednesday
Thursday 1
Friday
1.75
Saturday
2.5

30. frequency table help us collect, organize, and interpret data?
How might a
frequency table help us collect, organize, and interpret data?

31. The P.E. teacher asked the fourth graders to choose their favorite sport.7 6
Football
Baseball
Kia
James
Luke
Martin
Andy
Ryan
Lucas
Jarod
Jonah
Micah
Sara
Erin
Hadley 9 12
Kim
Soccer
Ben
Basketball
Skip
Lacey
Kate
Mary
Harper
Brook
Tara
Herb
Mason
Blake
Brie
Jake
Maddi
Noah
Blane
Jamie
Leah
Sophia
Nora

32. She created a frequency table to show the results.
Favorite Sports of 4th Graders at Maple Elementary
Sports
Tally
Frequency
Baseball 7
Football 6
Soccer 9
Basketball 12

33. On Friday, the students were asked to turn in their reading logs for the past two months. Maci’s log showed the hours she read each week.
Weeks in March
Hours
March 1 - 5 6
March
March 5
March
March 4
Weeks in April
Hours
April 1 - 2 3
April 3 - 9 6
April 5
April
April

34. using decimals or fractions.
Maci chose to use fractions to represent part of an hour. The same information could be represented
using decimals or fractions.
Weeks in March
Hours
March 1 - 5 6
March
March 5
March
March 4
Weeks in April
Hours
April 1 - 2 3
April 3 - 9 6
April 5
April
April

35. She recorded the hours from least to greatest and created a frequency table to show the results.
3, 4, 5, 5, 5 , 6, 6, 6 , 6 , 6
Hours Maci Read in March and April
Hours
Tallies
Frequency 3 1 4 5 2 6

36. Let’s Practice . . . Mr. Wright is a banker. One of his
customers is often late making his car payment. Mr. Wright made a list of the customer’s payment history.
Number of Days the Customer was Late to Pay for 20 Months 2 3 5 4 1
Use the customer’s payment history and create a frequency table.

37. Compare Your Answer
Number of Days the Customer was Late to Pay for 20 Months 2 3 5 4 1
Number of Days Payment was Late
Days
Tallies
Frequency 4 1 2 3 5 7

38. dot plot help us collect, organize, and interpret data?
How might a
dot plot help us collect, organize, and interpret data?

39. Mr. Garcia asked the students to write their names in the appropriate column to show the number of pets they have.
No Pets pet pets pets pets pets pets
Carlos
Andy
Hadley
Maddi
Jarod
Ryan
Lucas
Sophia
Ben
Erin
Jonah
Brie
Juan
Luke
Lacey
Sara
James
Brook
Kim
Leah
Kia
Laney
Nora
Lyn
Skip
Jake
Blane
Kate
Tara
Harper
Mary
Martin
Herb
Noah
Blake
Jamie

40. Number of Pets Each Student Has
Then, Mr. Garcia created a dot plot to organize the information he collected.
Number of Pets Each Student Has
= 2 Pets
Be careful to notice
the key.
Turn to your partner and discuss … How many students have 1 pet? How many students have 3 pets? How many students have 2 or more pets? 12 6 18

41. Number of Pets Each Student Has
You may also see a dot plot that uses “X”s instead of dots.
Number of Pets Each Student Has
x = 2 Pets
x x x x x x x x
x x x x
x x x x x x
When drawing dot plots be careful to line up the dots or “x”s in a straight line and try to keep them the same size so their value will appear accurate at a glance.

42. Let’s Practice . . .
Can you interpret the information on this dot plot and answer the questions correctly?
Miles Dad Traveled Each Day for 60 Days x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ^ ^
| | | | | | | | | | | | | | | x = 2 days
1. How many days did Dad drive 5.25 miles?
2. What mileage was driven most often? 3. How many days did Dad drive more than miles?

43. Compare Your Answer 6 days 5.75 miles 13 days
Miles Dad Traveled Each Day for 60 Days x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ^ ^
| | | | | | | | | | | | | | | x = 2 days
1. How many days did Dad drive 5.25 miles?
2. What mileage was driven most often? 3. How many days did Dad drive more than miles?
6 days
5.75 miles
13 days

44. A Few Important Reminders . . .
* Data is information collected about people, objects or events.
* Numerical data is represented with labels and may be whole numbers, fractions or decimals.
* A title clarifies the meaning of the data.
* Be overly cautious about the key. It is very important for interpreting the problem correctly.

45. Congratulations!
You can collect, organize, and interpret data using stem-and-leaf plots, frequency tables, and dot plots!

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