11.2B Box-and Whisker Plots
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11.2B Box- 11.2B Box- and and Whisker Whisker Plots Plots
description
11.2B Box-and Whisker Plots. Objectives. To get a more complete picture of the data. Be able to figure out the first quartile, third quartile, and interquartile range. Introduction. The purpose of calculating a mean or median is to obtain one number that describes some measurements. - PowerPoint PPT Presentation
Transcript of 11.2B Box-and Whisker Plots
11.2B Box-11.2B Box-and and Whisker Whisker PlotsPlots
ObjectivesObjectives
• To get a more complete picture of the data.
• Be able to figure out the first quartile, third quartile, and interquartile range.
IntroductionIntroduction
• 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.
DefinitionsDefinitions
• A box-and-whisker plot is a graph that gives a more complete picture of the data. It shows five numbers:
1. The smallest value2. The first quartile3. The median,4. The third quartile and5. The greatest value
First/Third Quartile First/Third Quartile definitionsdefinitions
• 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.
ExampleExample
• Find the first quartile Q1 and the third quartile Q3 for the prices of 15 half-gallon cartons of deluxe ice cream. 3.2
64.71
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.
ExampleExample
• Find the first quartile Q1 and the third quartile Q3 for the prices of 15 half-gallon cartons of deluxe ice cream. 3.2
64.71
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
4.45
4.56
4.71
4.83
5.44
5.49
The median is 4.29.
ExampleExample
Now separate the data into two groups. Those values below the median and those values above the median.
4.36
4.45
4.56
4.71
4.83
5.44
5.49
2.39
2.66
3.18
3.26
3.58
3.86
4.18
Values less than median Values greater than median
Q1Q3
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
Interquartile Range Interquartile Range DefinitionDefinition
• Is the difference between the third quartile Q3 and the first quartile Q1. Interquartile range =
Q3 – Q1 = 4.71 – 3.26 = 1.45
Fifty percent of the data in a distribution lie in the interquartile range.
Box-and-Whisker Box-and-Whisker PlotsPlots
• 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.
2.39 3.26 4.29 4.715.49
Q1 Q3Median
Box-and-Whisker Box-and-Whisker PlotsPlots
• 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).
2.39 3.26 4.29 4.715.49
Q1 Q3
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
Median
ExampleExample
• 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 Find the first quartile and third quartile for the data in the software quartile for the data in the software
training table.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.
ExampleExample
• 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
24
30
35
38
38
40
43
45
46
48
53
54
62
64
Arrange data from least to greatest.
Find the medianFind the median24
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 = 44
2
Next find the median of the Next find the median of the top lower half and the upper top lower half and the upper
half. half. 24
30
35
38
38
40
43
Median = 53; so Q3 = 53
Median =38; so Q1 = 38
45
46
48
53
54
62
64
Draw the Line and plot Draw the Line and plot pointspoints
24 38 44 5364
Draw a box – neatly and Draw a box – neatly and label 1label 1stst and 3 and 3rdrd quartile and quartile and
medianmedian
24 38 44 5364
Q1 Q3
Median
