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Math

Question Find the mean score of 66 students with scores 9090, 1717 students with scores 8080, and 1313 students with scores 7070. Round the answer to at least one decimal place.

Studdy Solution

STEP 1

Assumptions
1. The number of students and their corresponding scores are given in the table.
2. The mean score is calculated by dividing the sum of all scores by the total number of students.
3. The scores are weighted by the number of students who achieved them.

STEP 2

Calculate the total score for each group of students by multiplying the number of students by their respective score.
Total score for 90=Number of students×Score=6×90Total\, score\, for\, 90 = Number\, of\, students \times Score = 6 \times 90

STEP 3

Calculate the total score for the students who scored 90.
Total score for 90=6×90=540Total\, score\, for\, 90 = 6 \times 90 = 540

STEP 4

Calculate the total score for the students who scored 80.
Total score for 80=17×80=1360Total\, score\, for\, 80 = 17 \times 80 = 1360

STEP 5

Calculate the total score for the students who scored 70.
Total score for 70=13×70=910Total\, score\, for\, 70 = 13 \times 70 = 910

STEP 6

Add up all the total scores to get the combined total score.
Combined total score=Total score for 90+Total score for 80+Total score for 70Combined\, total\, score = Total\, score\, for\, 90 + Total\, score\, for\, 80 + Total\, score\, for\, 70

STEP 7

Calculate the combined total score.
Combined total score=540+1360+910Combined\, total\, score = 540 + 1360 + 910

STEP 8

Calculate the combined total score.
Combined total score=540+1360+910=2810Combined\, total\, score = 540 + 1360 + 910 = 2810

STEP 9

Calculate the total number of students by adding the number of students in each score group.
Total number of students=6+17+13Total\, number\, of\, students = 6 + 17 + 13

STEP 10

Calculate the total number of students.
Total number of students=6+17+13=36Total\, number\, of\, students = 6 + 17 + 13 = 36

STEP 11

Now, calculate the mean score by dividing the combined total score by the total number of students.
Mean score=Combined total scoreTotal number of studentsMean\, score = \frac{Combined\, total\, score}{Total\, number\, of\, students}

STEP 12

Plug in the values for the combined total score and the total number of students to calculate the mean score.
Mean score=281036Mean\, score = \frac{2810}{36}

STEP 13

Calculate the mean score.
Mean score=281036≈78.06Mean\, score = \frac{2810}{36} \approx 78.06

STEP 14

Round the mean score to at least one decimal place.
Mean score≈78.1Mean\, score \approx 78.1
The mean score is approximately 78.1.

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