Box & Whisker Plots SDAP 1.3 (Understand the meaning of, and be able to compute the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set).
Heat vs. Lakers 3/4/12 T. Murphy 0 points S. Blake 3 points A. Goudelock 7 points A. Bynum 16 points K. Bryant 33 points
Heat vs. Lakers 3/4/12 Minimum Value 0 First Quartile 3 Median 7 Third Quartile 16 Maximum Value 33
What is a box & whisker plot? A box-and-whisker plot ◦can be useful for handling many data values ◦allow people to explore data and to draw informal conclusions when two or more variables are present ◦show only certain statistics rather than all the data Think back on the Lakers… did the box-and- whisker plot show rebounds? Fouls? Free throws?
Step One: Find the Median (middle) The following numbers are the amount of marbles different boys own To find the median, put the numbers in order & find the one in the exact middle
Step Two: The Lower Quartile Focus only on the values to the left of the median: Now we need to find the median of these numbers ◦Since they’re already in order it’s easy to see the median of the values less than the median is 52 This value is called the “Lower Quartile” ◦Think ahead: Using your knowledge of prefixes and suffixes, what does ‘quartile’ mean and how will knowing this help us design our box- and-whisker plot?
Step Three: The Lower Quartile Now consider only the values to the right of the median: You should have noticed the median of this set of numbers is 87 This value is called the “Upper Quartile”
Wait a minute… Too easy right? What happens if you’re finding the median in an ordered set with an even number of values? ◦You must first take the average of the two middle numbers. For example: 3, 5, 7, and 10. Add the two middle numbers = 12 Divide your answer by the number of values added 12 / 2 = 6 6 is the average and your median for this set.
Step Four: The Interquartile Range You’re now ready to find the Interquartile Range (IQR). The IQR is the difference between the upper quartile and the lower quartile. In our case the IQR = 87 – 52 IQR = 35 The IQR is a very useful measurement because it is less influenced by extreme values, it limits the range to the middle 50% of the values.
Step Five: Draw Your Graph X
Now you try!
#1 What is the median of the set of data below? 34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12 34
#2 What is the upper quartile of the set of data below? 34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12 41
#3 What is the maximum value (upper extreme) of the set of data below? 34, 22, 18, 32, 26, 56, 49, 40, 34, 41, 12 56
DROPS ON A PENNY! partner activity You will need: ◦Cup of water ◦Penny ◦Paper towel ◦Eye dropper ◦4 sticky notes ◦Pencil
Directions Working with a partner, take turns dropping one drop of water at a time on the penny. Both partners count the drops as you go to assure for an accurate count. When the water finally spills over the edge of the penny record on your sticky note how many drops you had before the water spilled Each partner will take 2 turns Be sure to dry the penny between turns When your team is done, clean up and construct a box-and-whisker plot for your information. ◦When everyone is finished we will make one for the class’ results!