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Homework Questions
Quiz!• Shhh….• Once you are finished you can work on the warm-
up (grab a handout)!
Section 1.3Numerical Summaries of Distributions
(Quantitative)
Numerical Summaries• A numerical summary of a distribution should
report at least its center, and spread, or variability.
• A statistic is resistant if it is relatively unaffected by extreme observations.
The Meano Mean () being the average, is not a resistant
measure of center.• We use the equation for the mean.
• Using the mean as a measure of center dictates we use standard deviation as a measure of spread.
The MedianMedian (M) being the midpoint of the data set is a resistant measure of center.
We just count to the middle value (averaging the two middle values if there is an even number within the data set).
Example: 5 10 10 10 10 12 15 20 20 25 30 30 40 40 60Example:10 30 5 25 40 20 10 15 30 20 15 20 85 15 65 15 60 60 40 45
Comparing Mean & Median• For a symmetric distribution, the mean and
median are equal
Comparing Mean & Median
• For a distribution skewed to the right, the mean is to the right of the median
Comparing Mean & Median
• For a distribution skewed to the left, the mean is to the left of the median.
Interquartile Range• The IQR of a data set is the difference between , and
, so literally . This is referred to as the interquartile range, and is a resistant measure of spread.
• Example: 5, 8, 4, 4, 6, 3, 8 • Put them in order: 3, 4, 4, 5, 6, 8, 8
• Half way is the Q2
• Half of the 1st half is Q1
• Half of the 2nd half is Q3
• IQR = Q3 - Q1
Find the IQR and the 5 Number
Summary• Five Number Summary –
o Minimum, Q1, Median, Q3, Maximum
• 1, 3, 3, 4, 5, 6, 6, 7, 8, 8
Box Plot• You can use the 5 Number Summary to create a
box plot of the data.
Your turn…• Find the 5 number summary, IQR, and create a
box plot of the data• 85, 91, 99, 101, 105, 109, 111, 119, 125
Outliers• If an observation falls outside of 1.5 x IQR, then it
is an outlier.• For example, 85, 91, 99, 101, 105, 109, 111, 119,
125• IQR was _________• 1.5 x IQR = • Do we have any outliers?
Homework• Pg. 70 (80, 82-88, 90-96)