1. Statistics: Describing Quantitative Data Box and Whisker Plots

2. Do Now Complete Problem #2 in the stem and leaf packet regarding American vs. National baseball averages.

3. Questions?!?! Any questions on stem and leaf plots in general? Ask now!!! Please!

4. Box and Whisker Plots Displays 5 pieces of information: – 1. Minimum – 2. Q1 – 3. Median – 4. Q3 – 5. Maximum

5. Q1/Q3 Q1/Q3: The medians of the lower/upper half of the data. – Upper Quartile/Lower Quartile – 25 th /75 th percentile

6. IQR Interquartile Range: – IQR= Q3 – Q1 Another way to describe spread IF you describe center as the median, use IQR as the measure for spread.

7. Creating Box/Whisker Plots Create a vertical axis Draw in a horizontal line to indicate Q1, median and Q3. Create a box around them. Determine the “fences” – Q3+1.5IQR – Q1-1.5IQR – NOTE: Anything outside these fences is considered an outlier! So it will be drawn in with a special (i.e. *) symbol. Complete the display with whiskers to the min/max of the data INSIDE the fences, then add on *’s as needed for the outliers.

8. Example One: In 1961 Roger Maris made baseball headlines by hitting 61 home runs, breaking a famous record held by Babe Ruth. Here are Maris’s home run totals for his 10 seasons. Create a box and whisker plot to display the data. Would you consider his record-setting year to be an outlier? 8 131416232628333961

9. Interpreting Box Plots

10. Overall Symmetric Data: – The mean/median should be close together – The boxplot should be relatively symmetrical Skewed Left: – The median will be smaller than the mean – The median will be closer to Q3 than Q1 – The left whisker will be longer than the right Skewed Right: – The median will be larger than the mean – The median will be closer to Q1 than Q3 – The right whisker will be longer than the left.

11. Example Three: Percent on Time Count48 Mean68.35 Median69.90 Standard Deviation10.20 Min43.20 Max87.40 Range44.20 25 th Percentile59.15 75 th Percentile74.75

12. Practice Problems Try some on your own/in small groups

13. Exit Ticket Is the following data skewed or symmetric. If skewed, tell me which way. EXPLAIN yourself. Count45 Mean5892.91 Standard Deviation386.59 Minimum5185 Q15585.75 Median5928 Q36131 Maximum6796