Question

the following scores represent students test grades in ms. orrs science class.

what is the median score for ms. orrs science class?
i dont know yet
87
91
81
84

Explanation:

Step1: Count the number of data points

First, we count how many test scores there are. Let's list out the scores: 78, 87, 78, 87, 78, 87, 78, 87, 81, 91, 81, 91, 81, 91, 81, 91? Wait, no, looking at the table, let's count the rows. Wait, the table has two columns? Wait, no, maybe I misread. Wait, the left column: 78, 81, 78, 81, 78, 81, 78, 81, 78 (that's 9 rows? Wait, no, the table as shown: let's count the number of entries. Wait, each cell is a score? Wait, maybe the table is two columns, but let's list all scores:

Looking at the left column (first column) and right column (second column):

First column: 78, 81, 78, 81, 78, 81, 78, 81, 78 (wait, no, the first column has 78 (row1), 81 (row2), 78 (row3), 81 (row4), 78 (row5), 81 (row6), 78 (row7), 81 (row8), 78 (row9). Wait, no, the second column: 87 (row1), 91 (row2), 87 (row3), 91 (row4), 87 (row5), 91 (row6), 87 (row7), 91 (row8), 87 (row9). Wait, so total number of scores: 9 (first column) + 9 (second column)? No, that can't be. Wait, maybe each row has two scores? Wait, the problem says "students' test grades", so maybe each cell is a grade. Let's count the number of cells:

Looking at the table:

Row 1: 78, 87

Row 2: 81, 91

Row 3: 78, 87

Row 4: 81, 91

Row 5: 78, 87

Row 6: 81, 91

Row 7: 78, 87

Row 8: 81, 91

Row 9: 78, 87

Wait, that's 9 rows, each with 2 scores, so total 18 scores? Wait, no, maybe I miscounted. Wait, let's list all scores:

78, 87,

81, 91,

78, 87,

81, 91,

78, 87,

81, 91,

78, 87,

81, 91,

78, 87.

So let's list them in order:

First, collect all scores:

78 (row1), 87 (row1),

81 (row2), 91 (row2),

78 (row3), 87 (row3),

81 (row4), 91 (row4),

78 (row5), 87 (row5),

81 (row6), 91 (row6),

78 (row7), 87 (row7),

81 (row8), 91 (row8),

78 (row9), 87 (row9).

Now, let's sort all these scores in ascending order:

First, count the frequency of each score:

78: let's see, row1, row3, row5, row7, row9: that's 5 times? Wait, row1:78, row3:78, row5:78, row7:78, row9:78: 5 times.

81: row2, row4, row6, row8: 4 times.

87: row1, row3, row5, row7, row9: 5 times? Wait, row1:87, row3:87, row5:87, row7:87, row9:87: 5 times.

91: row2, row4, row6, row8: 4 times.

Wait, total scores: 5 (78) + 4 (81) + 5 (87) + 4 (91) = 18 scores.

Now, to find the median, we need the middle value(s) when the data is sorted. For 18 data points (even number), the median is the average of the 9th and 10th values.

Let's list the sorted scores:

78, 78, 78, 78, 78,

81, 81, 81, 81,

87, 87, 87, 87, 87,

91, 91, 91, 91.

Wait, let's index them:

1:78

2:78

3:78

4:78

5:78

6:81

7:81

8:81

9:81

10:87

11:87

12:87

13:87

14:87

15:91

16:91

17:91

18:91

Wait, no, that's not right. Wait, 5 78s, then 4 81s, then 5 87s, then 4 91s. So the order is:

Positions 1-5: 78

Positions 6-9: 81 (since 5+4=9)

Positions 10-14: 87 (9+5=14)

Positions 15-18: 91 (14+4=18)

Wait, so the 9th value is 81 (position 9: 81), and the 10th value is 87 (position 10: 87). Wait, no, wait:

Wait, 5 78s: positions 1-5.

Then 4 81s: positions 6-9 (5+4=9).

Then 5 87s: positions 10-14 (9+5=14).

Then 4 91s: positions 15-18 (14+4=18).

So the 9th term is 81 (position 9: 81), 10th term is 87 (position 10: 87). Wait, but median for even number of data points is the average of the (n/2)th and (n/2 +1)th terms. Here n=18, so n/2=9, n/2 +1=10. So median is (81 + 87)/2 = 84? Wait, but the options include 84. Wait, but maybe I made a mistake in counting the number of scores.

Wait, maybe the table is 9 rows, each with two scores, but maybe I miscounted the number of rows. Wait, looking at the image, the left column has 9 entries (78,81,78,81,78,81,78,81,78) and the right column has 9 entries (87,91,87,91,87,91,87,91,87). So total 18 scores.

But let's check again. Wait, maybe the table is actually 9 rows, each with one score? No, the table has two columns. Wait, maybe the problem is that the scores are 78,81,78,81,78,81,78,81,78,87,91,87,91,87,91,87,91,87. Wait, that's 18 scores.

But let's sort them:

78,78,78,78,78,81,81,81,81,87,87,87,87,87,91,91,91,91.

Now, n=18, so median is average of 9th and 10th terms.

9th term: 81 (since first 5 are 78, next 4 are 81: 5+4=9, so 9th term is 81)

10th term: 87 (next 5 are 87: 9+1=10, so 10th term is 87)

So median = (81 + 87)/2 = 84. Wait, but the options include 84. But let's check again. Wait, maybe I made a mistake in the number of scores.

Wait, maybe the table is 9 rows, each with two scores, but maybe the actual number of students is 9, and each student has two scores? No, that doesn't make sense. Wait, maybe the table is a typo, and it's 9 scores? Wait, no, the image shows 9 rows, two columns.

Wait, alternatively, maybe the scores are: 78,87,78,87,78,87,78,87,78,87,81,91,81,91,81,91,81,91. Wait, that's 18 scores.

But let's check the options: the options are 87,91,81,84.

Wait, maybe I miscounted the number of scores. Let's count again:

Looking at the left column (first column) of the table:

Row 1: 78

Row 2: 81

Row 3: 78

Row 4: 81

Row 5: 78

Row 6: 81

Row 7: 78

Row 8: 81

Row 9: 78

That's 9 scores: 78,81,78,81,78,81,78,81,78.

Right column (second column):

Row 1: 87

Row 2: 91

Row 3: 87

Row 4: 91

Row 5: 87

Row 6: 91

Row 7: 87

Row 8: 91

Row 9: 87

That's 9 scores: 87,91,87,91,87,91,87,91,87.

So total 18 scores. Now, let's sort all 18 scores:

78,78,78,78,78,81,81,81,81,87,87,87,87,87,91,91,91,91.

Now, the median is the average of the 9th and 10th terms.

9th term: 81 (since first 5 are 78, next 4 are 81: 5+4=9, so 9th term is 81)

10th term: 87 (next 5 are 87: 9+1=10, so 10th term is 87)

So median = (81 + 87)/2 = 84.

Wait, but let's check again. Wait, maybe the table is 9 scores, not 18? Maybe each row is a student, and the two columns are two different tests? But the problem says "test grades", maybe it's one test. Wait, maybe the table is actually 9 scores, with some repetition. Wait, no, the left and right columns are separate. Wait, maybe the question is considering all scores, so 18 scores. Then median is 84.

But let's check the options: the options are 87,91,81,84. So 84 is an option.

Wait, but maybe I made a mistake in the number of scores. Let's count the number of entries:

Left column: 9 entries (78,81,78,81,78,81,78,81,78)

Right column: 9 entries (87,91,87,91,87,91,87,91,87)

Total: 18 entries. So n=18, even. So median is average of 9th and 10th.

Sorted list:

78 (5 times), 81 (4 times), 87 (5 times), 91 (4 times).

So positions 1-5: 78

Positions 6-9: 81 (5+4=9)

Positions 10-14: 87 (9+5=14)

Positions 15-18: 91 (14+4=18)

So 9th term: 81 (position 9)

10th term: 87 (position 10)

Median: (81 + 87)/2 = 84.

So the answer should be 84.

Wait, but let's check again. Maybe the table is 9 scores, with the two columns being a mistake. Wait, if we consider only the left column: 78,81,78,81,78,81,78,81,78 (9 scores). Then sorted: 78,78,78,78,78,81,81,81,81. Median is 5th term: 78. But that's not an option.

If we consider only the right column: 87,91,87,91,87,91,87,91,87 (9 scores). Sorted: 87,87,87,87,87,91,91,91,91. Median is 5th term: 87. Which is an option, but that doesn't make sense.

Alternatively, maybe the table is 9 rows, each with two scores, but the question is considering each student's average? No, the question says "median score", so it's the median of all scores.

Wait, maybe I miscounted the number of scores. Let's count the number of cells:

Looking at the image, the table has 9 rows and 2 columns, so 18 cells, each with a score. So 18 scores. Then median is (81 + 87)/2 = 84. So the answer is 84.

Answer:

84