Download 4-28 Statistics: Chapter 4 Review A – KEY 1. Describe when it is

Statistics: Chapter 4 Review A – KEY
1. Describe when it is more accurate to use the median and IQR to measure the center and spread
of a set of data opposed to using the mean and standard deviation.
If a distribution is skewed or has outliers, use the median and IQR instead of mean and standard deviation.
2. Below are four histograms from www.shodor.org/interactivate. For each display, choose
whether it more accurate to use the median and IQR, the mean and standard deviation, or
either. Also estimate the mean and median for each using the histograms.
College Math SAT scores
Summarize with median and IQR.
The median is approximately 500, with the mean
slightly higher, perhaps approximately 520.
Body Fat of 252 men
Summarize with either median and IQR or mean
and standard deviation.
The median is approximately 18% body fat, with
the mean slightly higher, perhaps 19% body fat.
NBA Payrolls
Summarize with median and IQR.
The median is approximately $24 million, with the
mean higher, perhaps $30 million.
Horsepower of Cars
Summarize with median and IQR.
The median is approximately 90 horsepower, with the
mean higher, perhaps 130 horsepower.
3. Imagine in the last histogram, if the car with the highest horsepower was “souped” up so that it
now has 300 horsepower. How would each of the following summary statistics change: mean,
median, range, IQR, and standard deviation?
The mean, range, and standard deviation would all increase. The median and IQR would not change.
160
101
101
88
4. Here are the number of floors in the 16 tallest buildings of the
world. On the back make a histogram of this data, find the five
number summary, and write a full shape, center, spread
description in context (use the W’s!!!)
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88
88
96
80
69
102
78
70
Number of Floors in 16 Tallest Buildings
5
4
Frequency
Min = 66
Q1 = 78.5
Median = 88
Q3 = 101.75
Max = 160.
The distribution of the number of floors in the
worlds 16 tallest buildings is roughly unimodal and
slightly skewed to the left. The median number of
floors is 88 and the IQR is 23.25 floors. The
distribution contains an outlier (Burj Khalifa in
Dubai, UAE) that has 160 floors. This is 50 floors
more than the next highest number of floors.
88
66
110
103
3
2
1
0
80
100
120
Number of Floors
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley.
140
160