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Range, Quartiles, Box, and Whisker Plots

Range, Quartiles, Box, and Whisker Plots. Example. In a full marathon, run in Saskatoon on Saturday, September 6, 1997, severe wind conditions affected the finishing times. The women, ages 20-29, had times (rounded to the nearest minute) as shown in the table below. Example.

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Range, Quartiles, Box, and Whisker Plots

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  1. Range, Quartiles, Box, and Whisker Plots

  2. Example • In a full marathon, run in Saskatoon on Saturday, September 6, 1997, severe wind conditions affected the finishing times. The women, ages 20-29, had times (rounded to the nearest minute) as shown in the table below.

  3. Example • To find the range, subtract the smallest number from the largest 291 – 205 = 86 minutes Arrange the data in increasing order:  The lower quartile, median, and upper quartile will divide the data into 4 groups

  4. Example 205 220 230 249 260 263 267 291  Start by finding the median  Mark the spot where the median divides the data into two parts  Now, find the median of the numbers to the left of the marker  Now, find the median of the numbers to the right of the marker

  5. Example • The value of the lower quartile is 225 • The value of the median is 254.5 • The value of the upper quartile is 265 205 220 230 249 260 263 267 291 Lower quartile - 225 Median – 254.5 Upper quartile - 265

  6. Example • An outlier is any value in the data set that is more than 1.5 interquartile ranges above the upper quartile or below the lower quartile. • A 50 % box and whisker plot contains the upper and lower extremes, the quartiles, and the median.

  7. Example • To draw a box and whisker plot, draw a uniformly scaled number line that contains all of the data. 1) We then draw a box above the number the extends from the lower quartile (225) to the upper quartile (265) 205 225 245 265 285 305 2) Next, draw a vertical line at the median 254.5 3) Last, add the whiskers which extend from the lower quartile to the lower extreme (205) and from the upper quartile to the upper extreme (291)

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