Question

jan is a leading player on her basketball team. she has kept track of how many points she has scored over the course of the season. her scores may be viewed in the table below.
20 19 24 41 34 23 15 22
32 28 18 18 14 14 12 16

what is the median of jans scores?
a. 18
b. 19.5
c. 20
d. 21.875

Explanation:

Step1: Count the number of scores

First, we count how many scores there are. Let's list out the scores: 20, 19, 24, 41, 34, 23, 15, 22, 32, 28, 18, 18, 14, 14, 12, 16. Counting them, we have 16 scores.

Step2: Sort the scores in ascending order

Now, we sort the scores from smallest to largest: 12, 14, 14, 15, 16, 18, 18, 19, 20, 22, 23, 24, 28, 32, 34, 41.

Step3: Find the median position

For a set with \( n \) elements, if \( n \) is even, the median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2} + 1) \)-th elements. Here, \( n = 16 \), so \( \frac{n}{2}=8 \) and \( \frac{n}{2}+1 = 9 \).

Step4: Identify the 8th and 9th elements

Looking at the sorted list:
1st: 12
2nd: 14
3rd: 14
4th: 15
5th: 16
6th: 18
7th: 18
8th: 19
9th: 20

Step5: Calculate the median

Now, we take the average of the 8th and 9th elements. The 8th element is 19 and the 9th is 20. The average is \( \frac{19 + 20}{2}=\frac{39}{2}=19.5 \).

Answer:

b. 19.5