Question Details

The mean marks of the following distribution is:

Marks Obtained No. of Students
36 12
35 11
93 18
17 5

Options

A

56

B

75

C

60

D

72

Show Answer

Correct Answer :

Option A

56

56

Solution :

To find the mean marks of the given distribution, we use the formula for the weighted mean (or arithmetic mean of a grouped frequency distribution):

Mean = ( f i · x i ) f i

where xi represents the marks obtained, and fi represents the number of students (frequency) for each mark.

Step 1: Calculate the total number of students (f)
Sum the frequencies in the "No. of Students" column:
f = 12 + 11 + 18 + 5 = 46

Step 2: Calculate the sum of the product of marks and number of students ((f·x))
Multiply each mark by its corresponding number of students and add the results:
( 36 · 12 ) = 432
( 35 · 11 ) = 385
( 93 · 18 ) = 1674
( 17 · 5 ) = 85

Now, sum these products:
( f · x ) = 432 + 385 + 1674 + 85 = 2576

Step 3: Calculate the mean
Divide the sum of the products by the total number of students:
Mean = 2576 46 = 56

Therefore, the mean marks of the distribution is 56.

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