a graphical presentation of the five-number summary of data Box-and-Whisker Plot a graphical presentation of the five-number summary of data

Making a Box-and-Whisker Plot Draw a vertical scale including the lowest and highest values. To the right of the scale, draw a box from Q1 to Q3 (from lower to upper quartile). Draw a solid line through the box at the median (Q2). Draw lines (whiskers) from Q1 to the lowest and from Q3 to the highest values.

Computing Quartiles Order the data from smallest to largest. Find the median, the second quartile (Q2). Find the median of the data falling below Q2. This is the first quartile (Q1) Find the median of the data falling above Q2. This is the third quartile (Q3).

Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 The data has been ordered. The median is 24.

Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 The data has been ordered. The median is 24.

Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 For the data below the median, the median is 17. 17 is the first quartile.

Find the quartiles: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 For the data above the median, the median is 33. 33 is the third quartile.

Find the interquartile range: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 IQR = Q3 – Q1 = 33 – 17 = 16 The IQR represents the range of the middle 50% of the data. In the box plot, it refers to the length of the box.

Construct a Box-and-Whisker Plot: 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 51 Lowest = 12 Q1 = 17 median = 24 Q3 = 33 Highest = 51

Box-and-Whisker Plot Lowest = 12 Q1 = 17 median = 24 Q3 = 33 Highest = 51 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 -

Identifying Outliers Find IQR (Interquartile Range) Multiply IQR times 1.5 Determine the length of each whisker If a whisker length is greater than 1.5 times IQR, then an outlier is present in that whisker. Indicate outlier with a symbol (*). Redraw whisker to the next value. Go back to step 3 to determine if there exists any additional outliers. If both whisker lengths are NOT greater than 1.5 times the IQR, then any outliers have been identified.

Example: Original data with a minor change. 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 61 Lowest = 12 Q1 = 17 median = 24 Q3 = 33 Highest = 61

Example: Original data with a minor change. 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 61 IQR = Q3 – Q1 = 33 – 17 = 16 1.5(16) = 24 Lower Whisker = 5; Upper Whisker = 28 Since Upper Whisker > 1.5(IQR), outlier present.

Box Plot without identifying the Outlier 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 - 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 61 Lowest = 12 Q1 = 17 median = 24 Q3 = 33 Highest = 61

“Modified” Box Plot: Outlier Identified 60 - 55 - 50 - 45 - 40 - 35 - 30 - 25 - 20 - 15 - 10 - * 12 15 16 16 17 18 22 22 23 24 25 30 32 33 33 34 41 45 61 Lowest = 12 Q1 = 17 median = 24 Q3 = 33 Highest = 61