Download Measuring Variability

Measuring Variability
Example 1
WEATHER The data below represents the daily high temperature in Brownville for a period of 15
days in degrees Fahrenheit.
63 72
81 73 67
62 70 71 68
66
73 65
78
66
60
a. Find the interquartile range of the temperatures.
b. Find the semi-interquartile range of the temperatures.
a. First, order the data from least to greatest, and identify the quartiles.
60 62
63 65 66
66 67 68 70
71
72 73
73
78
81
Q1 = 65
Q2 = 68
Q3 = 73
The interquartile range is 73 – 65 or 8. This means that the middle half of the temperatures are
between 65 and 73 and are within 8 degrees of each other.
8
b. The semi-interquartile range is 2 or 4.
Example 2
WEATHER Draw a box-and-whisker plot for the temperatures in Example 1.
Draw a number line and plot the quartiles, the median, and the extreme values. Draw a box to show the
interquartile range. Draw a segment through the median to divide the box into two smaller boxes.
Before drawing the whiskers, determine if there are any outliers. These are temperatures that are more
than 12 degrees above 73 or more than 12 degrees below 65. There are no outliers.
Example 3
WEATHER Refer to the data in Example 1. Find the mean deviation of the temperatures.
1
There are 15 temperatures listed and the mean is 15(1035) or 69.
15
X 69
MD 1
15 i 1 i
1
MD 15(71) or about 4.73
This value could also be found using a
graphing calculator. Enter the data in L1.
At the home screen, enter the following
formula.
sum(abs(L1 – 69))/15
Example 4
WEATHER Refer to the data in Example 1. Find the standard deviation of the temperatures.
There are 15 temperatures listed and the mean is 69.
1
15
15
X 1 69
2
i 1
5.60
The standard deviation is about 5.60.
This value can also be found using a
graphing calculator. Enter the data in L1.
Press and then select the CALC option
from the menu to find the 1-variable
statistics.
Example 5
TRAFFIC Use the frequency distribution data below to find the arithmetic mean and the standard
deviation of highway speeds for 50 vehicles.
Class
Limits
50 – 60
60 – 70
70 – 80
80 – 90
Class
Marks (X)
55
65
75
85
f
f X
X
6
23
14
7
50
330
1495
1050
595
3470
-14.4
-4.4
5.6
15.6
X
3470
The mean is 50 or 69.4.
The standard deviation is
3832
50 or approximately 8.75.
This value can also be found using a graphing
calculator. Enter the class marks in L1 and the
frequency in the L2 list. Press and then select
the CALC option from the menu to find the 1variable statistics.
X
X
207.36
19.36
31.36
243.36
2
X
X
1244.16
445.28
439.04
1703.52
3832
f