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Q
uantitative
R
easoning &
P
roblem
S
olving
296
© 2014 Pacific Crest
Scenario 1:
Symmetric Data
A fashion designer wants to know the average height of their female clients.
They will use this information as part of the design process.
Step
Watch it Work!
1.
Describe the
data set
The following is a list of heights of 16 randomly selected female clients of a
fashion designer. Unit is inches and rounded to the nearest inch.
66 65 69 66 64 72 66 64 67 62 68 62 68 65 65 64
2.
Describe the
type of data
Heights of women are ratio level of measurement. The differences are relevant
and 0 inches means the complete lack of height.
3.
Construct a
histogram or bar
graph
2
4
6
8
10
12
64
70 72
62
66 68
74
Use technology to construct a
histogram. Determine if the data
has outliers or if it is skewed.
There are no outliers. The data
does not seem to be symmetric.
There is not a long tail on one side
so we cannot say for certain that
the data set is skewed.
4.
Determine which
measures of CT
are reasonable
Since the data is ratio interval of measurement, the mean, median and mode are
reasonable.
The data set is neither symmetric nor strongly skewed so both the mean and
median may be reasonable.
5.
Compute the
measures of CT
and determine
which is best
To compute the mean, add the numbers in the data set and divide by the number
of elements in the data set.
66 + 65 + 69 + 66 + 64 + 72 + 66 + 64 + 67 + 62 + 68 + 62 + 68 + 65 + 65 + 64 = 1053
1053
Mean
65.8125
16
= =
There is an even number of elements in this sorted set so there are two numbers
straddling the middle.
62 62 64 64 64 65 65
65
66
66 66 67 68 68 69 72
The median is obtained by adding those together and dividing by 2.
65 66
Median
65.5
2
+
=
=
Notice that the mean and median are similar but not identical. Both measures are
reasonable in this example.
The mode corresponds to the date element that appears most often. In this
example 64, 65, and 66 are all modes since they appear three times. The mode
may not be useful in this context.