collect marks of 10 of your classmates in different subjects in the recent examination. estimate the arithmetic mean of marks in each subject and verify them by actual calculations.how many of your estimations represent exact mean?
To estimate the arithmetic mean of marks in each subject, you need to collect the marks of 10 of your classmates in different subjects. Let's assume you have collected the following marks:
Subject A:
Classmate 1: 85
Classmate 2: 75
Classmate 3: 90
Classmate 4: 80
Classmate 5: 92
Classmate 6: 78
Classmate 7: 86
Classmate 8: 84
Classmate 9: 88
Classmate 10: 81
Subject B:
Classmate 1: 90
Classmate 2: 85
Classmate 3: 88
Classmate 4: 79
Classmate 5: 93
Classmate 6: 82
Classmate 7: 87
Classmate 8: 89
Classmate 9: 91
Classmate 10: 83
To estimate the arithmetic mean in each subject, add up all the marks for each subject and then divide by the total number of classmates.
For Subject A:
(85 + 75 + 90 + 80 + 92 + 78 + 86 + 84 + 88 + 81) / 10 = 849 / 10 = 84.9
For Subject B:
(90 + 85 + 88 + 79 + 93 + 82 + 87 + 89 + 91 + 83) / 10 = 847 / 10 = 84.7
The estimations for the arithmetic mean in Subject A and Subject B are 84.9 and 84.7 respectively.
To verify these estimates by actual calculations, add up all the marks for each subject and then divide by the total number of classmates.
For Subject A:
[ (85 + 75 + 90 + 80 + 92 + 78 + 86 + 84 + 88 + 81) / 10 ] = 849 / 10 = 84.9
For Subject B:
[ (90 + 85 + 88 + 79 + 93 + 82 + 87 + 89 + 91 + 83) / 10 ] = 847 / 10 = 84.7
By performing the actual calculations, both estimations for the arithmetic mean in Subject A and Subject B are exact. So, both of your estimations represent the exact mean.
To estimate the arithmetic mean of marks in different subjects, collect the marks of 10 classmates for each subject in the recent examination. Then, calculate the sum of the marks for each subject and divide it by the total number of students (which is 10).
For example, let's say you have collected the following marks in three subjects for 10 classmates:
Subject A: 80, 75, 85, 90, 78, 83, 88, 84, 91, 77
Subject B: 70, 65, 74, 80, 68, 79, 75, 81, 72, 73
Subject C: 90, 88, 92, 85, 89, 86, 91, 88, 90, 93
To estimate the arithmetic mean, sum up the marks for each subject:
Subject A: 80 + 75 + 85 + 90 + 78 + 83 + 88 + 84 + 91 + 77 = 831
Subject B: 70 + 65 + 74 + 80 + 68 + 79 + 75 + 81 + 72 + 73 = 717
Subject C: 90 + 88 + 92 + 85 + 89 + 86 + 91 + 88 + 90 + 93 = 892
Then, divide the sum by the total number of students (10) to find the estimated arithmetic mean:
Estimated mean for Subject A: 831 / 10 = 83.1
Estimated mean for Subject B: 717 / 10 = 71.7
Estimated mean for Subject C: 892 / 10 = 89.2
To verify these estimations, calculate the actual arithmetic mean using all the marks collected for each subject:
Actual mean for Subject A: (80 + 75 + 85 + 90 + 78 + 83 + 88 + 84 + 91 + 77) / 10
Actual mean for Subject B: (70 + 65 + 74 + 80 + 68 + 79 + 75 + 81 + 72 + 73) / 10
Actual mean for Subject C: (90 + 88 + 92 + 85 + 89 + 86 + 91 + 88 + 90 + 93) / 10
Now, compare the estimated means with the actual means and determine how many estimations represent exact means. If the estimated mean matches the actual mean, then consider it as an exact mean. If they are slightly different, it shows a variation in estimation.
For example, if the actual means for the subjects are:
Actual mean for Subject A: 82.1
Actual mean for Subject B: 70.5
Actual mean for Subject C: 90.3
In this case, the estimated mean for Subject A (83.1) represents an exact mean since it matches the actual mean (82.1). However, the estimated mean for Subject B (71.7) and Subject C (89.2) do not represent exact means as they deviate slightly from the actual means (70.5 and 90.3).
Siddhartha
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