Chapter 20: Measures of Center and Spread 283CHECK POINT
In questions 16–18, find the first quartile, median, and third quartile of each
data set.- A = {3, 4, 5, 4, 7, 8, 9, 2, 10, 17, 32, 34, 36, 38}
- B = {2, 2, 3, 3, 4, 4, 4, 34, 54, 78, 92, 101}
- C = {22, 83, 21, 49, 76, 64, 83, 29, 94, 19, 82, 28, 101}
- George and Harry take the same test. George’s score places him at
the 54th percentile, and Harry’s score is at the 43rd percentile. Who did
better? - Draw a box plot for data set A in question 16.
The Spread
It’s good to know where the center of your data is. That tells you the average value. But only
knowing the center of your data is like only knowing the center of a circle. You know where it is,
but you don’t really know what it looks like, because you don’t know how big it is. You can’t draw
the circle until you know the center and the radius, and you don’t have a good picture of your
data until you know the center and the spread.
Measures of spread tell you whether all the numbers are clumped up close to the average or
whether they’re spread all over the place. If, over the course of the semester, you earned test
scores of 69, 70, 73, 74, and 74, you’d have a mean score of 72 and a median score of 73. If you
earned test scores of 43, 61, 73, 85 and 98, you’d also have a mean score of 72 and a median of 73,
but the two sets of scores give very different pictures of how your semester went. Knowing how
spread out the numbers are can also be important information.Range
The simplest measure of the spread is called the range. It’s just the difference between the
highest value and the lowest value. Those test scores of 69, 70, 73, 74, and 74 have a range of
74 – 69 = 5, but the scores of 43, 61, 73, 85, and 98 have a range of 98 – 43 = 55. The much larger
range for the second set tells you that the numbers varied a great deal. The smaller range says
that the numbers clumped up fairly close to the mean or median.