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)