Statistics: Describing Quantitative Data Box and Whisker Plots

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

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

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

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

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.

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.

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?

Interpreting Box Plots

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.

Example Three: Percent on Time Count48 Mean68.35 Median69.90 Standard Deviation10.20 Min43.20 Max87.40 Range th Percentile th Percentile74.75

Practice Problems Try some on your own/in small groups

Exit Ticket Is the following data skewed or symmetric. If skewed, tell me which way. EXPLAIN yourself. Count45 Mean Standard Deviation Minimum5185 Q Median5928 Q36131 Maximum6796