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SecTIoN 1D Describing Quantitative Data with Numbers 69

Manufacturer Apple Samsung Apple 83.45 3.762 Min Q 1 Median Q 3 Max IQR
x
s x
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87
83
86
73
84
3
Samsung
79.87
83
86
62
11
6.74
75
88
60 65 70 75 80 85 90
Overall rating
Compare the distributions of overall rating for Apple and Samsung.
SOLUTION:
Shape: Both distributions of overall rating are skewed to the left.
Be sure to discuss shape, outliers, center, and
Outliers: There are two low outliers in the Apple tablet distri- variability, and to include context (variable
bution with overall ratings of 73 and 76. The Samsung tablet name)!
distribution has no outliers.
Center: The Apple tablets had a slightly higher median overall Don’t forget to explicitly compare measures of
rating (84) than the Samsung tablets (83). More importantly, center and variability, using words like “greater
about 75% of the Apple tablets had overall ratings that were than,” “less than,” or “about the same as.”
greater than or equal to the median for the Samsung tablets. Due to the strong skewness and outliers, use
the median and IQR instead of the mean and
Variability: There is much more variation in overall rating among standard deviation when comparing center and
the Samsung tablets than among the Apple tablets. The IQR variability.
for Samsung tablets (11) is almost four times larger than the
IQR for Apple tablets (3).
FoR PRAcTIce, TRY eXeRcISe 35

AP® EXAM TIP
Use statistical terms carefully and correctly on the AP® Statistics exam. Don’t say “mean” if
you really mean “median.” Range is a single number; so are Q , Q , and IQR. Avoid sloppy
3
1
use of language, like “the outlier skews the mean” or “the median is in the middle of the
IQR.” Skewed is a shape and the IQR is a single number, not a region. If you misuse a term,
expect to lose some credit.

Here’s an activity that gives you a chance to use the skills you have learned in this
unit: selecting statistical methods, data analysis, and making statistical arguments.

ACTIVITY Team challenge: Did Mr. Starnes stack his class?

In this activity, you will work in a team of three or four students to resolve a dispute.
®
Mr. Starnes teaches AP Statistics, but he also does the class scheduling
®
for the high school. There are two AP Statistics classes — one taught by Mr.
Starnes and one taught by Ms. McGrail. The two teachers give the same first

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