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Math

QuestionCalculate the mean score from the following data, rounded to the nearest tenth: 65 (9), 70 (2), 75 (6), 80 (2), 85 (3), 90 (7), 95 (7).

Studdy Solution

STEP 1

Assumptions1. The scores of the students are given in the table. . The number of students who got each score is also given in the table.
3. We need to find the mean of the scores.

STEP 2

The mean of a set of numbers is calculated by summing all the numbers and dividing by the count of numbers. But in this case, we have a frequency table, so we need to multiply each score by its frequency (number of students) before summing.
Mean=∑(Score×Frequency)Total number of studentsMean = \frac{\sum (Score \times Frequency)}{Total\, number\, of\, students}

STEP 3

First, we need to find the total number of students. We can do this by summing the frequencies.
Total number of students=9+2+6+2+3+7+7Total\, number\, of\, students =9 +2 +6 +2 +3 +7 +7

STEP 4

Calculate the total number of students.
Total number of students=9+2+6+2+3+7+7=36Total\, number\, of\, students =9 +2 +6 +2 +3 +7 +7 =36

STEP 5

Next, we need to calculate the sum of the product of each score and its frequency.
∑(Score×Frequency)=65×9+70×2+75×+80×2+85×3+90×7+95×7\sum (Score \times Frequency) =65 \times9 +70 \times2 +75 \times +80 \times2 +85 \times3 +90 \times7 +95 \times7

STEP 6

Calculate the sum of the product of each score and its frequency.
∑(Score×Frequency)=65×9+70×2+75×6+80×2+85×3+90×+95×=2975\sum (Score \times Frequency) =65 \times9 +70 \times2 +75 \times6 +80 \times2 +85 \times3 +90 \times +95 \times =2975

STEP 7

Now, we can calculate the mean by dividing the sum of the product of each score and its frequency by the total number of students.
Mean=∑(Score×Frequency)Total number of students=297536Mean = \frac{\sum (Score \times Frequency)}{Total\, number\, of\, students} = \frac{2975}{36}

STEP 8

Calculate the mean to the nearest tenth.
Mean=297536≈82.6Mean = \frac{2975}{36} \approx82.6The mean score of the students on the exam is approximately82.6.

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