Quartiles and the Interquartile Range

 Comparing shape, center, and spreads of two or more distributions  Distribution has too many values for a stem plot or dot plot  You don’t need to see individual values, even approximately  You don’t need to see more than a five number summary, but would like outliers clearly indicated

 Minimum  Lower or 1 st Quartile  Median  Upper or 3 rd Quartile  Maximum

Lower quartile (Q 1 ) = median of the lower half of the data set. Upper Quartile (Q 3 ) = median of the upper half of the data set. The interquartile range (iqr), is a resistant measure of variability given by: Note: If n is odd, the median is excluded from both the lower and upper halves of the data.

 15 students with part time jobs were randomly selected and the number of hours worked last week was recorded. 19, 12, 14, 10, 12, 10, 25, 9, 8, 4, 2, 10, 7, 11, 15 The data is put in increasing order to get 2, 4, 7, 8, 9, 10, 10, 10, 11, 12, 12, 14, 15, 19, 25

 With 15 data values, the median is the 8 th value, which is ________. 2, 4, 7, 8, 9, 10, 10, 10, 11, 12, 12, 14, 15, 19, 25 Lower HalfUpper Half Lower quartile Q 1 Median Upper quartile Q 3 The IQR =

 An observation is an outlier if it is more than 1.5 IQR away from the closest end of the box (less than the lower quartile minus 1.5 IQR or more than the upper quartile plus 1.5 IQR.  Formulas:

 A boxplot represents outliers by shaded circles. Whiskers extend on each end to the most extreme observations that are not outliers.  Calculator notes:  1. Select the boxplot with the dots  2. Hit ZoomStat (Zoom 9)  3. Use the Trace button to locate the median, quartiles, upper and lower fences, and outliers (if present).

9  Using the student work hours data we have Lower quartile IQR = (6) = -1 Upper quartile IQR = (6) = 23 Smallest data value that isn’t an outlier Largest data value that isn’t an outlier Upper quartile + 3 IQR = (6) = 32 Mild Outlier

10  Consider the ages of 79 students. IQR = 22 – 19 = Median Lower Quartile Upper Quartile Moderate Outliers Extreme Outliers Lower quartile – 1.5 IQR =14.5 Upper quartile IQR= 26.5

11 Smallest data value that isn’t an outlier Largest data value that isn’t an outlier Mild Outliers Extreme Outliers Here is the boxplot for the student age data.

Here is the same boxplot reproduced with a vertical orientation.

Females Males GenderGender Student Weight By plotting boxplots of two separate groups or subgroups we can compare their distributional behaviors. Notice that the distributional pattern of female and male student weights have similar shapes, although the females are roughly 20 lbs lighter (as a group).

14 Mean

 What is another name for the 2 nd quartile?  What would a boxplot look like for a data set that is skewed right? Left? Symmetric?