California Standards Test (CST), 2007

Source:  California Standards Test (CST), Grade 7, 2007

Question:

95.  Jared scored the following numbers of points in his last 7 basketball games: 8, 21, 7, 15, 9, 15, and 2.  What is the median number of points scored by Jared in these 7 games?

A.    9
B.   11
C.   15
D.   19

Answer:  A


What Are The Flaws in This Question?

  1. The numbers of points are hard to read and comprehend because they are embedded in the paragraph.  Also, in the actual test booklet, the line break comes after the second 15, so that the "2" is on the next line.  Students may get the wrong answer because they don't see the "2."  
  2. Option C is a bad wrong choice because 15 is both the mode of the numbers and the middle number in the *unordered* list.  It is a common mistake for students to confuse the median with the mode, and it is also common to neglect to order the numbers before determining the median.  If a student chooses option C, there is no way to know which mistake the student made.


How to Fix This Question:

First of all, the numbers should not be embedded in the paragraph.  They should be on a separate line.

Secondly, the numbers should be changed so that the middle number in the unordered list and the mode are not the same.  In the actual question, 11 (option B) is the mean, which is a good wrong choice because students often make the common mistake of confusing the mean and median.  The number 19 (option D) is the range, which is okay as a wrong choice but is probably not as common a mistake as the mean, mode, and middle number, so it could be eliminated (however, it would be okay to include it instead of the mode).  So I would eliminate that choice and have the mode and middle number instead.

Here is how I would rewrite the question, with the explanations for the wrong answers inside the brackets (see Example 11 in my book, which is very similar to this question and discusses the same issues as above):

95 Revised.  Jared scored the following numbers of points in his last 7 basketball games:

                      8,   21,   7,   15,   9,   7,   10

What is the median number of points scored by Jared in these 7 games?

A.    7         [mode]
B.    9         [median - correct answer]
C.   11        [mean]
D.   15        [middle number in unordered list]

Answer:  B