Measures of Variation
The Range in the data set is
14, 16, 18, 24, 19, 15, 13
24-13=11
The lower quartile in the data set is
13, 14, 15, 16, 18, 19, 24
14
The outlier in the data set
20, 23, 18, 21, 4, 17, 15
4
What is a plot that uses a number line to show the distribution of a set of data by using five values.
a box-plot
Explain how to determine from a box-and-whisker plot whether there are any outliers in the data.
Outliers are shown as an asterisk beyond the extreme values, disconnected from the whisker of the box
The median in the data set is
29, 27, 24, 28, 30, 51, 28
28
The upper quartiele in the data set is
13, 14, 15, 16, 18, 19, 24
19
There are two outliers in the data set
22, 27, 25, 11, 29, 28, 41, 26, 28, 23.
11 and 41
This is drawn around the quartile values.
The box
Explain what the upper quartile is.
The median of the upper half of a set of data, represented by UQ, Q3
The outlier in the data set is
91, 92, 88, 89, 93, 95, 65, 85, 91
The interquartile range in the data set is
24, 27, 28, 28, 29, 30, 51
3
Data that are more than 1.5 times the value of the interquartile range beyond the quartiles.
Definition of outliers
These extend from each quartile to the extreme data points that are not outliers.
the whiskers
Explain what the lower quartile is.
The median of the lower half of a set of data, represented by LQ, Q1
The upper quartile in the data set is
132, 116, 108, 113, 126, 120, 131, 112, 126
128.5
The upper quartile in the data set is
90, 88, 72, 85, 92, 95, 93, 86, 92, 91
92
Find the outliers in the data set
42, 36, 58, 47, 34, 43, 54, 49, 48, 41, 38
none
Construct a box-and-whisker plot for the data set
4, 7, 5, 3, 9, 6, 4
Min= 3 Q1= 4 Median=5 Q3= 7 Max= 9
What percentage falls below Q1
25%
The lower quartile in the data set is
107, 114, 124, 108, 117, 106, 107, 109, 117, 115
107
Subtract the upper quartile from the lower quartile
The interquartile range
Describe how to find the limits for outliers.
Multiply the interquartile range by 1.5. Add that number to the upper quartile median and subtract it from the lower quartile median. Data that falls above or below the numbers are the outliers.
Construct a box-and-whisker plot for the data set
39, 41, 30, 14, 44, 40, 48, 39, 40, 36
Median= 40 Upper= 41 Lower= 36 Greatest= 48 Least= 30 Outlier= 14
The steps to create a box-and-whisker plot.
1.) Median, Greatest value, Least value 2.) Upper and lower quartile medians 3.) Interquartile range 4.) Outliers 5.) Create box-and-whisker plot