Question

question 1-18
22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72
find the median of the data above.
○ 84
○ 50.4
○ 54
○ 48

Explanation:

Step1: Sort the data

First, we sort the given data set in ascending order. The data is: 22, 28, 35, 36, 39, 39, 45, 48, 48, 53, 58, 67, 72, 82, 84. Wait, wait, let's count the number of data points. Let's list them again: 22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72. Let's count: 1 (22), 2 (84), 3 (36), 4 (48), 5 (28), 6 (39), 7 (53), 8 (67), 9 (82), 10 (58), 11 (39), 12 (35), 13 (45), 14 (48), 15 (72). So 15 data points. Now sort them: 22, 28, 35, 36, 39, 39, 45, 48, 48, 53, 58, 67, 72, 82, 84.

Step2: Find the median position

For a data set with \( n \) values, the median is the value at position \( \frac{n + 1}{2} \) when \( n \) is odd. Here, \( n = 15 \), so the position is \( \frac{15 + 1}{2} = 8 \).

Step3: Identify the median

Looking at the sorted data, the 8th value is 48? Wait, no, wait. Wait, let's list the sorted data again carefully:

1. 22
2. 28
3. 35
4. 36
5. 39
6. 39
7. 45
8. 48
9. 48
10. 53
11. 58
12. 67
13. 72
14. 82
15. 84

Wait, the 8th value is 48? But wait, let's check again. Wait, maybe I made a mistake in sorting. Let's re-sort:

Original data: 22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72.

Let's sort step by step:

Start with 22. Then 28 (since 28 >22). Then 35 (35>28). Then 36 (36>35). Then 39 (39>36), then another 39 (39=39). Then 45 (45>39). Then 48 (48>45), then another 48 (48=48). Then 53 (53>48). Then 58 (58>53). Then 67 (67>58). Then 72 (72>67). Then 82 (82>72). Then 84 (84>82). So the sorted list is: 22, 28, 35, 36, 39, 39, 45, 48, 48, 53, 58, 67, 72, 82, 84. So 15 numbers. The median is the 8th number. The 8th number is 48? Wait, but let's check the options. Wait, maybe I miscounted the data points. Wait, let's count the original data: 22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72. Let's count: 1.22, 2.84, 3.36, 4.48, 5.28, 6.39, 7.53, 8.67, 9.82, 10.58, 11.39, 12.35, 13.45, 14.48, 15.72. Oh! Wait, I made a mistake in sorting earlier. Oh no, that's the error. Let's sort correctly. Let's list all numbers:

22, 28, 35, 36, 39, 39, 45, 48, 48, 53, 58, 67, 72, 82, 84. Wait, no, the original data includes 84, 82, 72, 67, 58, 53, 48, 48, 45, 39, 39, 36, 35, 28, 22. Wait, let's list all 15 numbers:

1. 22
2. 28
3. 35
4. 36
5. 39
6. 39
7. 45
8. 48
9. 48
10. 53
11. 58
12. 67
13. 72
14. 82
15. 84

Yes, that's correct. So the 8th term is 48? But wait, the options include 48 as one of the choices. Wait, but let's check again. Wait, maybe I missed a number. Wait, original data: 22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72. Let's count: 22 (1), 84 (2), 36 (3), 48 (4), 28 (5), 39 (6), 53 (7), 67 (8), 82 (9), 58 (10), 39 (11), 35 (12), 45 (13), 48 (14), 72 (15). Oh! Wait, I see the mistake. I had 84, 67, 82, 58 in the wrong order. Let's sort correctly:

Start with the smallest:

22 (1)

28 (2)

35 (3)

36 (4)

39 (5)

39 (6)

45 (7)

48 (8)

48 (9)

53 (10)

58 (11)

67 (12)

72 (13)

82 (14)

84 (15)

Ah! There we go. I had 67, 82, 58 in the wrong order before. So the correct sorted list is: 22, 28, 35, 36, 39, 39, 45, 48, 48, 53, 58, 67, 72, 82, 84. Now, \( n = 15 \), which is odd. The median is the \( \frac{15 + 1}{2} = 8 \)-th term. The 8th term is 48. Wait, but let's check the options. The options are 84, 50.4, 54, 48. So 48 is an option. Wait, but let me confirm again. Wait, maybe I miscounted the number of data points. Let's count the original data: 22, 84, 36, 48, 28, 39, 53, 67, 82, 58, 39, 35, 45, 48, 72. That's 15 numbers. So sorted, the 8th is 48. So the median is 48.

Answer:

48