Displaying & Analyzing Data

Stem-and-leaf PlotBox-and-Whisker PlotVenn Diagrams

Statistics: The branch of mathematics that deals with collecting, organizing, analyzing or interpreting data.Data: Numerical facts or information.Stem-and-Leaf Plots: A convenient method to display every piece of data by showing the digits of each number.

In a stem-and-leaf plot, the greatest common place value of the data is used to form stems. The numbers in the next greatest place value position are then used to form the leaves.

Age of United states Presidents at their First Inauguration: 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 50 47 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 (Through the 40th presidency)

Stem Leaf

4

5

6

9

07

9

1

77 7 1

6

68

8

4 42

8

41

0

7

45

2

1 6 15 4 1

5 0

3

5 6

2

2

1 9 4

2 3 6 7 8 9 9

0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8

0 1 1 1 2 4 4 5 8 9

Stem Leaf

4

5

6

Rearrange the leaf in numerical order from least to greatest

Rearrange the leaf in numerical order from least to greatest

Age of United states Presidents at their First Inauguration: 57 61 57 57 58 57 61 54 68 51 49 64 50 48 65 52 56 46 54 49 50 47 55 54 42 51 56 55 51 54 51 60 62 43 55 56 61 52 69 64 (Through the 40th presidency)

2 3 6 7 8 9 9

0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8

0 1 1 1 2 4 4 5 8 9

StemLeaf: Age of United States Presidents at their First Inauguration (through the 40th Presidency)

4

5

6

It is easy to interpret or analyze information from the Stem-and-Leaf.

1. How many presidents were 51 years old at their inauguration?

2. What age is the youngest president to be inaugurated?

3. What is the age of the oldest president to be inaugurated?

4. How many presidents were 40-49 years old at their inauguration?

44

4242

6969

77

Data Displays

A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set.

17, 18, 19, 21, 24,26, 27The lower quartile (LQ) is the median of the lower half of the data.The LQ is 18.The upper quartile (UQ) is the median of the upper half of the data. The UQ is 26.

17 18

19 20 21 22 23 24 25 26 282716

___ __

Make a Box & Whisker Plot

76, 78, 82, 87, 88, 88, 89, 90, 91, 95

88

Find the median of this segment (LQ)

LQ = 82

Find the median of this segment.

UQ = 90

76, 78, 82, 87, 88, 88, 89, 90, 91, 95

Now for the box and whisker

65 70 75 80 85 90 95

Least

Value

Lower Quartile (LQ)

Middle Quartil

e

Upper Quartil

e

Greatest

Value

100

105

76, 78, 82, 87, 88, 88, 89, 90, 91, 95

65 70 75 80 85 90 95

Least

Value

Lower Quartile (LQ)

Middle Quartil

e

Upper Quartil

e

Greatest

Value

100

105

What number represents 25% of the data?

What number represents 50% of the data?

What number represents 75% of the data?

LQ 82

Median 88

UQ 90

Venn Diagrams

Content Standard:

Begin to identify information in a Venn diagram

Click for the next screen.

The diagram shows the results of your survey on ice cream preferences for 23 friends.

13 81

Click for an answer.

How many of your friends liked chocolate and/or vanilla ice cream?How many students are not in the diagram? Why?

13 81

The End.

How many students are not in the diagram? Why? 23

-22

1

One student is not in the diagram. He must not like chocolate or vanilla ice cream.

Stem and Leaf Plot

Stem and leaf plots are used as a quick way of seeing how many pieces of data fall in various ranges. The reader can quickly tell:

- the range - the mode

Stem and leaf plots have a title, a stem, and leavesA key is used to explain how to read the stem and leaves.

Box - and - Whisker Plot

Displays large set of data.

Gives general idea of how data clusters.

Graph includes: - Title

- Labeled intervals - Box between lower

and upper quartiles - Whiskers from

quartiles to extremes - Median, quartiles

and whiskers labeled

Displaying & Analyzing Data

Stem-and-leaf PlotBox-and-Whisker PlotVenn Diagrams