Question

the following scores represent students test grades in ms. mihals fashion class.
78 88
83 92
78 88
83 92
78 88
83 92
78 88
83 92
78 88
what is the median score for ms. mihals fashion class?
85.5
i dont know yet
92
88
83

Explanation:

Step1: Count the number of data points

First, we count how many scores there are. Let's list them: 78 (5 times), 83 (4 times), 88 (5 times), 92 (4 times). Wait, actually, let's count the rows. Looking at the table, there are 9 rows? Wait, no, let's count the number of entries. Wait, the table has two columns? Wait, no, the left column and right column? Wait, no, the scores are: let's list all the scores. Let's see, each row has two numbers? Wait, no, maybe it's a table with two columns, but the scores are all the numbers. Wait, let's count the total number of scores. Let's see:

First column (left): 78, 83, 78, 83, 78, 83, 78, 83, 78. Wait, no, the first column: 78 (row 1), 83 (row 2), 78 (row 3), 83 (row 4), 78 (row 5), 83 (row 6), 78 (row 7), 83 (row 8), 78 (row 9). Then the second column (right): 88 (row 1), 92 (row 2), 88 (row 3), 92 (row 4), 88 (row 5), 92 (row 6), 88 (row 7), 92 (row 8), 88 (row 9). Wait, so total number of scores is 9 + 9 = 18? Wait, no, maybe each row is a student's two scores? No, the problem says "students' test grades", so maybe each cell is a grade. Let's count the number of cells: 9 rows, 2 columns, so 18 grades. Wait, but let's list all the grades:

78, 88,

83, 92,

78, 88,

83, 92,

78, 88,

83, 92,

78, 88,

83, 92,

78, 88.

So let's list them in order:

First, sort all the grades. Let's count the frequency:

78: how many times? Let's see, first column: 78 appears 5 times (rows 1,3,5,7,9), second column: no, wait, first column: rows 1,3,5,7,9: 5 times. Second column: 88 appears 5 times (rows 1,3,5,7,9). 83: first column rows 2,4,6,8: 4 times. 92: second column rows 2,4,6,8: 4 times. Wait, no, let's list all the numbers:

From the table, the numbers are:

78, 88,

83, 92,

78, 88,

83, 92,

78, 88,

83, 92,

78, 88,

83, 92,

78, 88.

So let's list them in order:

78, 78, 78, 78, 78,

83, 83, 83, 83,

88, 88, 88, 88, 88,

92, 92, 92, 92.

Wait, let's count: 78 (5), 83 (4), 88 (5), 92 (4). Total: 5+4+5+4=18. So 18 numbers. To find the median, we need the average of the 9th and 10th numbers when sorted.

Let's sort them:

First 5: 78,78,78,78,78

Next 4: 83,83,83,83

Next 5: 88,88,88,88,88

Next 4: 92,92,92,92

So the sorted list is:

1:78, 2:78, 3:78, 4:78, 5:78,

6:83, 7:83, 8:83, 9:83,

10:88, 11:88, 12:88, 13:88, 14:88,

15:92, 16:92, 17:92, 18:92.

Wait, no, wait: 5 (78s) + 4 (83s) = 9 numbers. Then the 10th number is the first 88. Wait, no:

Wait, 5 numbers of 78: positions 1-5.

Then 4 numbers of 83: positions 6-9 (since 5+4=9).

Then 5 numbers of 88: positions 10-14 (9+5=14).

Then 4 numbers of 92: positions 15-18.

So the 9th number is the last 83 (position 9), and the 10th number is the first 88 (position 10).

So median is (83 + 88)/2 = (171)/2 = 85.5? Wait, no, wait, that can't be. Wait, maybe I miscounted the number of scores. Wait, maybe each row is a student, so 9 students, each with two scores? No, the problem says "students' test grades", maybe it's a table with two columns, but the total number of grades is 18? Wait, but let's check again.

Wait, the table has 9 rows and 2 columns, so 18 cells. Let's list all the grades:

Row 1: 78, 88

Row 2: 83, 92

Row 3: 78, 88

Row 4: 83, 92

Row 5: 78, 88

Row 6: 83, 92

Row 7: 78, 88

Row 8: 83, 92

Row 9: 78, 88

So the grades are: 78,88,83,92,78,88,83,92,78,88,83,92,78,88,83,92,78,88.

Now, let's sort them in ascending order:

78,78,78,78,78,83,83,83,83,88,88,88,88,88,92,92,92,92.

Wait, now let's count the positions:

1:78

2:78

3:78

4:78

5:78

6:83

7:83

8:83

9:83

10:88

11:88

12:88

13:88

14:88

15:92

16:92

17:92

18:92

Ah, here we go. So the 9th term is 83 (position 9), and the 10th term is 88 (position 10). Therefore, the median is the average of the 9th and 10th terms: (83 + 88)/2 = 171/2 = 85.5. Wait, but the option is 85.5? Let me check the options. The options are: 85.5, I don't know yet, 92, 88, 83. So the correct answer should be 85.5.

Wait, but maybe I made a mistake in counting. Let's check the number of terms again. 18 terms, so median is the average of the 9th and 10th terms. Let's list the sorted list:

1:78

2:78

3:78

4:78

5:78 (5 terms)

6:83

7:83

8:83

9:83 (9 terms)

10:88

11:88

12:88

13:88

14:88 (14 terms)

15:92

16:92

17:92

18:92 (18 terms)

Yes, so 9th term is 83, 10th term is 88. So median is (83 + 88)/2 = 85.5.

Step2: Calculate the median

Since there are 18 scores (an even number), the median is the average of the 9th and 10th scores when sorted.

From the sorted list:
- The 9th score is 83.
- The 10th score is 88.

Median = \(\frac{83 + 88}{2} = \frac{171}{2} = 85.5\).

Answer:

85.5