Box and Whisker Plots Algebra 2

Box and Whisker Plot A box and whisker plot is a graphical display of the five number summary Draw a scale to include the lowest and highest data values Draw a box from Q1 to Q3 Include a solid line through the box at the median Draw solid lines, called whiskers from Q1 to the lowest value and from Q3 to the highest value.

Lowest Value or min Q1 Median (Q2) Q3 Highest value or max Five-Number Summary Lowest Value or min Q1 Median (Q2) Q3 Highest value or max

Quartiles Special percentiles (100% divided into fourths). So we consider data in the 25th percentile, quartile 1 (Q1) Median or 50th percentile, quartile 2 (Q2) 75th percentile, quartile 3 (Q3)

Is it an Outlier? Step 1: Find the inter-quartile range. Step 2: Multiply the IQR by 1.5. Step 3: Subtract the IQR #(1.5) from the first quartile. Any number less than this is an outlier. Step 4: Add the IQR #(1.5) from the third quartile. Any number above this is an outlier.

Things to Think About Which measure of central tendency is ALWAYS affected the most by an outlier? The mean. If there is NO outlier, which measure of central tendency is the best description of the data set? The mean. If there is an outlier, which measure of central tendency is the best description of the data set? Probably the median.

How to Compute Quartiles Order the data from smallest to largest. Find the median. This is the second quartile, Q2. The first quartile Q1 is the median of the lower half of the data; that is, it is the median of the data falling below Q2, but not including Q2 The third quartile Q3 is the median of the upper half of the data; that is, it is the median of the data falling above Q2 but not including Q2

Example 1-Consider the data set: {10, 20, 30 40, 50, 60, 70} The median, Q2 is 40 Q1 is the median of the values below 40, These values are 10, 20, and 30. The median, or Q1 is 20. Q3 is the median of the values above 40, These values are 50, 60 and 70 so the median or Q3 is 60.

Interquartile Range The interquartile range (IQR) is the difference between Q3 and Q1 or Q3 –Q1 For our data set Q1 is 20, Q3 is 60, so the interquartile range is 60-20 = 40

Five-Number Summary Example - For the data set {10,20,30,40,50,60,70}: The five number summary is Lowest number (min): 10 Q1: 20 Median (Q2): 40 Q3: 60 Highest number (max): 70

Graphing Calculator

TI 84 1-Variable Stats

TI 84 1-Variable Stats

TI 84 Box and Whisker Plot

TI 84 Box and Whisker Plot

TI 84 Box and Whisker Plot

TI 84 Box and Whisker Plot

TI 84 Box and Whisker Plot

TI 84 Box and Whisker Plot

Box-and-Whisker Plots Use the data to make a box and whisker plot. 3, 6, 7, 7, 2, 8, 3, 9, 11, 10, 9, 3, 4, 12, 2, 14, 7, 5, 10 Order the data: 2,2,3,3,3,4,5,6,7,7,7,8,8,9,10,10,11,12,14 Find the median and the medians of the upper and lower halves: 3, 7, 10. Check whether extremes are outliers. Plot the five values (minimum, maximum and the three quartiles). Draw the box and whiskers. 5 10 15 20 ●

Calculate Range and Inter-Quartile Range Use the data below. 2, 2, 3, 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 12, 14 Range – Maximum minus minimum. Thus, 14 - 2 = 12. IQR – Difference in Q3 and Q1. Thus 10 - 3 = 7. 5 10 15 20 ●

Lowest Value or min Q1 Median (Q2) Q3 Highest value or max Five-Number Summary Lowest Value or min Q1 Median (Q2) Q3 Highest value or max

Five-Number Summary Example - For the data set {10,20,30,40,50,60,70}: The five number summary is Lowest number, 10 Q1, 20 Median, 40 Q3, 60 Highest number, 70

Questions Is the median always in the middle of the box of your box and whiskers plot? How do outliers affect a box and whiskers plot? How can you use a box and whiskers plot to tell if your data is skewed right or skewed left? What would be a better way to display the data if you want to see the actual outliers?

Example 2 Compute the five-number summary and draw a box and whiskers plot for the test scores on a recent AP Statistics test {76, 59, 76, 78, 100,66,63,70,89,87,81,48,78} What scores if any might be considered outliers? How do they affect the shape of the graph? How would the graph change if you removed the outliers?

Example 3 Compute the five-number summary and draw a box and whiskers plot for the test scores on a recent AP Statistics test in another class. {87,78,91,70,70,66,87,78,80,86,97,98,97,94} What scores if any might be considered outliers? How do they affect the shape of the graph? How would the graph change if you removed the outliers? Compare the two sets of data? What can you conclude about the test results for the two classes?