collect marks of 10 of your classmates in different subjects in the recent examinations.estimate the arithmetic mean of marks in each subject and verify them by actual calculations.how many of your estimations represent exact mean
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To estimate the arithmetic mean of marks in each subject for your classmates, you will need to collect the marks for each subject from your 10 classmates. Let's say the subjects are Math, Science, and English.
Here's how you can estimate the arithmetic mean for each subject:
1. Collect the marks from each classmate for each subject.
Classmate 1: Math - 80, Science - 85, English - 90
Classmate 2: Math - 75, Science - 80, English - 85
Classmate 3: Math - 85, Science - 90, English - 95
Classmate 4: Math - 70, Science - 75, English - 80
Classmate 5: Math - 95, Science - 90, English - 85
Classmate 6: Math - 80, Science - 85, English - 90
Classmate 7: Math - 75, Science - 80, English - 85
Classmate 8: Math - 85, Science - 90, English - 95
Classmate 9: Math - 70, Science - 75, English - 80
Classmate 10: Math - 95, Science - 90, English - 85
2. Calculate the sum of marks for each subject.
Math: 80 + 75 + 85 + 70 + 95 + 80 + 75 + 85 + 70 + 95 = 800
Science: 85 + 80 + 90 + 75 + 90 + 85 + 80 + 90 + 75 + 90 = 840
English: 90 + 85 + 95 + 80 + 85 + 90 + 85 + 95 + 80 + 85 = 870
3. Estimate the arithmetic mean by dividing the sum of the marks by the number of classmates.
Math: 800 / 10 = 80
Science: 840 / 10 = 84
English: 870 / 10 = 87
Now, to verify the estimations by actual calculations:
4. Calculate the arithmetic mean of marks in each subject individually.
Math: (80 + 75 + 85 + 70 + 95 + 80 + 75 + 85 + 70 + 95) / 10 = 80
Science: (85 + 80 + 90 + 75 + 90 + 85 + 80 + 90 + 75 + 90) / 10 = 84
English: (90 + 85 + 95 + 80 + 85 + 90 + 85 + 95 + 80 + 85) / 10 = 87
By actual calculations, all of our estimations of the arithmetic mean for each subject match the exact mean.
Therefore, all of your estimations represent the exact mean.