1. Box & Whiskers Plots
AQR

2. Review Mean – Median – Mode –
Is the sum of the values in the set divided by the number of values. It is often represented as
Median –
Is the middle value or the mean of the two middle values when the set is ordered numerically
Mode –
Is the value or values that occur most often

3. A box-and-whisker plot shows the spread of a data set
A box-and-whisker plot shows the spread of a data set. It displays 5 key points: the minimum and maximum values, the median, and the first and third quartiles.

4. Box & Whiskers Plots Data is organized from smallest to largest.
Scale is based on data
Width of each segment of box indicates density of data
Wide segment means data frequency is not as dense
25% of the data is in each quartile
Quartiles can be found by using 1VARSTAT on calculator

5. How to construct find five-number summary Min Q1 Med Q3 Max
draw box from Q1 to Q3
draw median in the box
extend whiskers to min & max

6. Modified Box Plots Outlier Q3 Median Q1 670 590 530 Max Min 740 280
Verbal SAT scores
280, 340, 440, 490, 520, 540, 560, 560, 580, 580,
600, 610, 630, 650, 660, 680, 710, 730, 740, 740
Outlier Q1
530
Median
590 Q3
670
Min
280
Max
740

7. Modified boxplots display outliers fences mark off outliers
whiskers extend to largest (smallest) data value inside the fence

8. Calculating Outliers
IQR = Q3 – Q1 (IQR is a number, not a range of numbers)
IQR is the range of the middle 50% of the data
Outliers occur outside of “fences”
Data smaller than Q1 – 1.5*(IQR)
Data larger than Q *(IQR)
Each outlier is indicated with a dot, or asterix

9. Interquartile Range (IQR) – is the range (length) of the box
Outlier Fence
Q1 – 1.5(IQR)
Q (IQR)
Interquartile Range (IQR) – is the range (length) of the box
Q3 - Q1
Any observation outside this fence is an outlier! Put a dot for the outliers.

10. Modified Boxplot . . .
Draw the “whisker” from the quartiles to the observation that is within the fence!

11. Boxplots Organizes data into segments which is easy to quickly analyze
Useful for comparative displays
Convenient display of outliers
Great for large data sets
Should not be used for data sets smaller than 10
Raw data is lost
Can only estimate mean