The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest 10th.
Score: 60, 65, 70, 75, 80, 85, 90, 95
Number of Students 4, 2, 4, 5, 3, 3, 8, 3
To find the mean, we need to take the sum of all the scores and divide by the total number of students:
((60 x 4) + (65 x 2) + (70 x 4) + (75 x 5) + (80 x 3) + (85 x 3) + (90 x 8) + (95 x 3)) / (4 + 2 + 4 + 5 + 3 + 3 + 8 + 3)
= (240 + 130 + 280 + 375 + 240 + 255 + 720 + 285) / 30
= 2525 / 30
= 84.17
Rounding to the nearest 10th, the mean score is 84.2.
To find the mean of the scores, we need to multiply each score by the corresponding number of students, find the sum of these products, and then divide by the total number of students.
Let's calculate it step by step:
1. Multiply each score by the corresponding number of students:
60 * 4 = 240
65 * 2 = 130
70 * 4 = 280
75 * 5 = 375
80 * 3 = 240
85 * 3 = 255
90 * 8 = 720
95 * 3 = 285
2. Find the sum of these products:
240 + 130 + 280 + 375 + 240 + 255 + 720 + 285 = 2,525
3. Divide the sum by the total number of students:
4 + 2 + 4 + 5 + 3 + 3 + 8 + 3 = 32
2,525 / 32 ≈ 78.91
Therefore, the mean of the scores is approximately 78.91 when rounded to the nearest 10th.