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What is the mean of the following distribution?
| Marks | 13 | 23 | 51 | 61 | 96 |
|---|---|---|---|---|---|
| No. of Students | 51 | 34 | 62 | 87 | 17 |
46
72
37
34
46
Calculate the weighted average sum and divide by total students: (13∗51+23∗34+51∗62+61∗87+96∗17)/(51+34+62+87+17)=11776/251≈46.9. Rounded to nearest option 46.
Marks (x) = {13, 23, 51, 61, 96}, No. of Students (f) = {51, 34, 62, 87, 17}
x=∑fi∑fixi
Calculate the weighted average sum and divide by total students: (13∗51+23∗34+51∗62+61∗87+96∗17)/(51+34+62+87+17)=11776/251≈46.9. Rounded to nearest option 46.
Students often miscalculate the total number of students or make arithmetic errors in the sum of products (f*x).
Calculate sum of products
Find ∑fixi=(13×51)+(23×34)+(51×62)+(61×87)+(96×17)
663+782+3162+5307+1632=11546
Calculate sum of frequencies
Find total number of students ∑fi=51+34+62+87+17
∑fi=251
Calculate mean
Divide the total product sum by total students: x=11546/251
x=46
A is correct because the weighted mean of the provided frequency distribution is exactly 46.
This method is fundamental for calculating 'Expected Value' in Probability, which is a common topic in competitive exams like RRB JE.
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