Question

lisa 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
35	22
13	40
30	34
14	17
36	26
11	21

what is the median of lisa’s scores? round to the nearest point, if necessary.

a 23
b 24
c 26
d 30

please select the best answer from the choices provided

Explanation:

Step1: List all scores

First, we extract all of Lisa's scores from the table. Let's list them out: 36, 20, 35, 13, 30, 14, 36, 11, 29, 19, 22, 40, 34, 17, 26, 21. Wait, actually, looking at the table structure (two columns), let's count the number of rows. There are 8 rows? Wait, no, let's check again. Wait, the table has two columns, each with 8 entries? Wait, no, the left column (maybe first column) and right column? Wait, maybe the scores are: 36, 29, 20, 19, 35, 22, 13, 40, 30, 34, 14, 17, 36, 26, 11, 21? Wait, no, maybe each row has two scores? Wait, the problem says "how many points she has scored over the course of the season. Her scores may be viewed in the table below." So let's list all the scores: Let's take each cell as a score. So the scores are: 36, 29, 20, 19, 35, 22, 13, 40, 30, 34, 14, 17, 36, 26, 11, 21. Wait, that's 16 scores? Wait, no, maybe the table has two columns, each with 8 scores, so total 16 scores? Wait, let's count the number of entries: first column (top to bottom): 36, 20, 35, 13, 30, 14, 36, 11. Second column: 29, 19, 22, 40, 34, 17, 26, 21. So total 16 scores. Now, to find the median, we need to sort them in ascending order.

Step2: Sort the scores

Let's sort all the scores: 11, 13, 14, 17, 19, 20, 21, 22, 26, 29, 30, 34, 35, 36, 36, 40. Wait, let's check: 11, 13, 14, 17, 19, 20, 21, 22, 26, 29, 30, 34, 35, 36, 36, 40. Now, since there are 16 scores (even number), the median is the average of the 8th and 9th terms.

Step3: Find the 8th and 9th terms

Let's count the sorted list:

1: 11

2: 13

3: 14

4: 17

5: 19

6: 20

7: 21

8: 22

9: 26

10: 29

11: 30

12: 34

13: 35

14: 36

15: 36

16: 40

Wait, wait, that's 16 terms. So the 8th term is 22, 9th term is 26? Wait, no, wait, let's re-sort correctly. Wait, 11, 13, 14, 17, 19, 20, 21, 22, 26, 29, 30, 34, 35, 36, 36, 40. Wait, 1st:11, 2nd:13, 3rd:14, 4th:17, 5th:19, 6th:20, 7th:21, 8th:22, 9th:26, 10th:29, 11th:30, 12th:34, 13th:35, 14th:36, 15th:36, 16th:40. Wait, but the number of terms is 16, which is even, so median is (8th term + 9th term)/2. So 8th term is 22, 9th term is 26? Wait, no, wait, 22 is 8th, then 26 is 9th? Wait, no, between 22 and 26, what's next? Wait, 22, then 26? Wait, no, maybe I missed a score. Wait, let's list all scores again:

From the table:

First column (let's say left): 36, 20, 35, 13, 30, 14, 36, 11

Second column (right): 29, 19, 22, 40, 34, 17, 26, 21

So all scores: 36, 20, 35, 13, 30, 14, 36, 11, 29, 19, 22, 40, 34, 17, 26, 21

Now, let's sort them in ascending order:

11, 13, 14, 17, 19, 20, 21, 22, 26, 29, 30, 34, 35, 36, 36, 40

Yes, that's 16 scores. So the median is the average of the 8th and 9th terms.

8th term: 22

9th term: 26

Wait, no, wait: 11 (1), 13 (2), 14 (3), 17 (4), 19 (5), 20 (6), 21 (7), 22 (8), 26 (9), 29 (10), 30 (11), 34 (12), 35 (13), 36 (14), 36 (15), 40 (16). Wait, so 8th term is 22, 9th term is 26. Then median is (22 + 26)/2 = 24? Wait, but the options are 23, 24, 28, 30. Wait, (22 + 26)/2 = 24. So the median is 24.

Wait, but let's check again. Wait, maybe I made a mistake in the number of scores. Wait, maybe the table has 8 scores? Wait, no, the problem says "how many points she has scored over the course of the season" – maybe each row is a game, with two scores? No, that doesn't make sense. Wait, maybe the table is a list of scores, with two columns, but total 8 scores? Wait, no, the left column has 8 entries, right column has 8 entries, so 16 scores. Wait, but let's count the number of scores: 36,20,35,13,30,14,36,11,29,19,22,40,34,17,26,21 – that's 16 numbers. So sorted, 16 numbers, median is average of 8th and 9th. 8th is 22, 9th is 26. (22+26)/2=24. So the median is 24, which is option b.

Answer:

b. 24