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Box and Whisker Plots

Box and Whisker Plots

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Box and Whisker Plots

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  1. Box and Whisker Plots Module I, Lesson 5 Online Algebra VHS@PWCS

  2. Minimum Median Maximum Lower Quartile Upper Quartile Box and Whisker Plots A Box and Whisker Plot is a diagram that divides a set of data into 4 parts using the median and the quartiles.

  3. Median Review Recall from lesson 1.3, that a median is the number in the middle of a set of data, when it is put in order. Find the median of the following data: 24, 36, 21, 17, 18, 15, 29, 30, 15, 37 • Put the numbers in order from least to greatest. • Find the number in the middle. • Since there is no number in the middle, we find the mean of the 2 middle numbers. • 15, 15, 17, 18, 21, 24, 29, 30, 36, 37 • 3. (21 + 24)/2 • 45/2 • 22.5, is the median!

  4. Here is the middle (median) 17 is the median of the bottom half of the data. Therefore it is the Lower quartile Lower Quartile • Lower quartile – median of the lower half of the data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37

  5. Here is the middle (median) 30 is the median of the bottom half of the data. Therefore it is the Upper Quartile Upper Quartile • Upper quartile – median of the upper half of the data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37

  6. The box goes around these! What do you need for a Box and Whisker Plot? • Number Line • Minimum : smallest number • Lower quartile (LQ) • Median • Upper quartile (UQ) • Maximum: largest number. • Interquartile Range: UQ-LQ The whiskers go from the minimum to the lower quartile and the upper quartile to the maximum

  7. 14 18 22 26 30 34 38 Let’s make a Box and Whisker Plot. Here is our data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37 Step 1 – a number line Our data goes from 15 to 37, our number line can go from 14 to 38, with an interval of 2

  8. Let’s make a Box and Whisker Plot. Here is our data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37 Step 2 – Find the Values needed From our earlier calculations: • Minimum – 15 • Lower Quartile – 17 • Median – 22. 5 • Upper Quartile – 30 • Maximum -37 • Interquartile Range-13

  9. 14 18 22 26 30 34 38 Let’s make a Box and Whisker Plot. Here is our data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37 Step 3 – Plot the points a little above our number line • Minimum – 15 • Lower Quartile – 17 • Median – 22. 5 • Upper Quartile - 30 • Maximum - 37

  10. 14 18 22 26 30 34 38 Let’s make a Box and Whisker Plot. Here is our data 15, 15, 17, 18, 21, 24, 29, 30, 36, 37 Step 4– Draw the box and whiskers • Minimum – 15 • Lower Quartile – 17 • Median – 22. 5 • Upper Quartile - 30 • Maximum - 37

  11. Try this: Create a box-and-whisker plot of the following data (click for you answer when finished). 8, 15.5, 14, 14, 16, 18, 16.7, 15, 11.4, 16, 7

  12. 7 8 9 10 11 12 13 14 15 16 17 18 19 Is yours the same? 8, 15.5, 14, 14, 16, 18, 16.7, 15, 11.4, 16, 7 7, 8, 11.4, 14, 14, 15, 15.5, 16, 16, 16.7, 18 Lower Quartile Median Upper Quartile

  13. Data and Box-and-Whisker Plots • A box and whisker plot breaks the data into 4 equal parts. • 25% of the data is on the whisker from the minimum to the lower quartile • 25% of the data is in the box from the lower quartile to the median • 25% of the data is in the box from the median to the upper quartile • 25% of the data is on the whisker from the upper quartile to the maximum.

  14. 7 8 9 10 11 12 13 14 15 16 17 18 19 What do you know. • If 240 people at six flags were stopped and asked their age, how many people are older than 15? • 15 is the median and half of the data is above that so 120 people are older than 15. • Of those people how many were between 11 ½ and 15. • There are 60 people in that age range. (240/4)

  15. 7 8 9 10 11 12 13 14 15 16 17 18 19 What you don’t know. • If you are only given a box-and-whisker plot, you cannot see the following: • Mean – you need the individual data points and also the total • Mode – again you need the individual points • You can however find the range (maximum – minimum) • Or in this case 18 – 7, or 11.

  16. Box-and-Whisker Recap • A box-and-whisker plot divides data into 4 equal parts. • It will show the following: minimum, lower quartile, median, upper quartile, and maximum, You cannot find the mean or mode if you don’t have the individual data points • You can find the range by • Maximum - minimum • You can find the interquartile range by • Upper quartile – lower quartile