Homework Questions
Quiz!
• Shhh….
• Once you are finished you can work on the warmup (grab a handout)!
Section 1.3
Numerical 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 Mean
o Mean (𝒙) being the average, is not a resistant
measure of center.
• We use the equation 𝑥 =
1
𝑛
𝑥 for the mean.
• Using the mean as a measure of center
dictates we use standard deviation as a
measure of spread.
The Median
Median (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 60
Example:
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 𝑄3 , and
𝑄1 , so literally 𝑄3 − 𝑄1 . 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)