Math 2311
Class Notes for Section 1.4
More measures of spread (or dispersion):
•
Range –
Drawbacks of range:
sensitivity to
outliers
•
Percentiles:
o
25
th
percentile, Q1 –
o
50
th
percentile, Median or Q2 –
o
75
th
percentile, Q3 –
The values of the minimum, Q1, Q2, Q3 and the maximum make up what is called our
five number
summary
.
•
IQR –
Example:
1. Twelve babies spoke for the first time at the following ages (in months):
8 9 10 11 12 13 15 15 18 20 20 26
Find Q1, Q2, Q3, the range and the IQR.
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The IQR is used to determine data classified as
outliers
. An outlier is an observation that is “distant” from the
rest of the data. Outliers can occur by chance or be measurement errors so it is important to identify them.
Any point that falls outside the interval calculated by Q1 1.5(IQR) and Q3 + 1.5(IQR) is considered an
outlier.
Example:
2.
Are there any outliers in the data set given for example 1?
If so, what are they?
There are other percentiles as well. The
k
th percentile
means that
k
% of the ordered data values are at or
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 Spring '08
 HAFEEZ

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