Download 11.2b Box And Whisker Plots

11.2B Boxand Whisker
Plots
Statistics
Mrs. Spitz
Fall 2008
Objectives
• To get a more complete picture of
the data.
• Be able to figure out the first
quartile, third quartile, and
interquartile range.
Assignment
11.2B
Introduction
• The purpose of calculating a
mean or median is to obtain one
number that describes some
measurements.
• That one number alone;
however, may not adequately
represent the data.
Definitions
•
A box-and-whisker plot is a
graph that gives a more
complete picture of the data. It
shows five numbers:
1.
2.
3.
4.
5.
The smallest value
The first quartile
The median,
The third quartile and
The greatest value
First/Third Quartile
definitions
• Symbolized by Q1, the number
below which one-quarter of the
data lie. The third quartile,
symbolized by Q3 is the number
above which one-quarter of the
data lie.
Example
• Find the first quartile Q1 and the third
quartile Q3 for the prices of 15 halfgallon cartons of deluxe ice cream.
3.26
4.71
4.18
4.45
5.49
3.18
3.86
3.58
4.29
5.44
4.83
4.56
4.36
2.39
To find the quartiles, first arrange the data from the smallest
value to the largest value. Then find the median.
2.66
Example
• Find the first quartile Q1 and the third
quartile Q3 for the prices of 15 halfgallon cartons of deluxe ice cream.
3.26
4.71
4.18
4.45
5.49
3.18
3.86
3.58
4.29
5.44
4.83
4.56
4.36
2.39
2.66
To find the quartiles, first arrange the data from the smallest
value to the largest value. Then find the median.
2.39
2.66
3.18
3.26
3.58
3.86
4.18
4.29
4.36
The median is 4.29.
4.45
4.56
4.71
4.83
5.44
5.49
Example
Now separate the data into two groups. Those values
below the median and those values above the median.
Values less than median
2.39
2.66
3.18
3.26
Q1
3.58
3.86
Values greater than median
4.18
4.36
4.45
4.56
4.71
4.83
5.44
Q3
The first quartile Q1 is the median of the lower half of the data: Q1 = 3.26
The third quartile Q3 is the median of the upper half of the data: Q3 = 4.71
5.49
Interquartile Range
Definition
• Is the difference between the
third quartile Q3 and the first
quartile Q1. Interquartile range =
Q3 – Q1 = 4.72 – 3.26 = 1.45
Fifty percent of the data in a distribution lie in the
interquartile range.
Box-and-Whisker Plots
• Shows the data in the
interquartile range as a box. The
box-and-whisker plot for the data
on the cost of ice cream is shown
below.
Q1
2.39
3.26
Median
4.29
Q3
4.71
5.49
Box-and-Whisker Plots
• Note that the box-and-whisker plot labels
five values: the smallest (2.39); the first
quartile Q1 (3.26), the median (4.29); the
third quartile Q3, 4.71; and the largest value
(5.49).
Q1
2.39
3.26
Median
4.29
Q3
4.71
5.49
Recall from the last section that the difference
between the largest and smallest values is called the
RANGE. For these data: Range = 5.49 – 2.39 =
3.10
Example
• For these next two
examples, use the data
in the following table. I
am putting it vertically,
so you can read it.
30
45
54
24
48
38
43
38
46
53
62
64
40
35
Find the first quartile and third quartile for
the data in the software training table.
Strategy:
• Arrange the data from smallest to
largest. Then find the median
• Find Q1 as the median of the lower
half of the data.
• Find Q3 as the median of the upper
half of the data.
• Draw a box and whiskers plot for the
data in the software training table.
Example
• For these next two
examples, use the data
in the following table. I
am putting it vertically,
so you can read it.
30
54
45
24
48
43
46
62
38
38
53
64
40
35
Arrange data from least to greatest.
24 30 35 38 38 40 43 45 46 48 53 54 62 64
Find the median
24 30 35 38 38 40 43 45 46 48 53 54 62 64
Oops, there are an even number, so you must take the two
middle numbers, add them together and divide by 2.
Median = 43 + 45
2
= 44
Next find the median of the top
lower half and the upper half.
24 30 35 38 38 40 43
Median =38; so Q1 = 38
45 46 48 53 54 62 64
Median = 53; so Q3 = 53
Draw the Line and plot
points
24
38
44
53
64
Draw a box – neatly and label 1st
and 3rd quartile and median
Q1
24
38
Median
44
Q3
53
64
Homework Answers
1.Mean = 19
Median = 19.5
9. 72 yds.
2.Mean = 381.56
Median =394.5
10. 21
3. Mean = 10.61
Median = 10.605
11. 77
4.Mean = 45.615
Median = 45.855
12. 2
5. Median
13. German
6. mean – 88.3
Median = 94
14. brown
7.Mean = 17.45
Median = 17
15. Satisfactory
8.Mean =403.63
Median =411
16. very good