What is the mean of the following distrubution?

Marks	10	28	48	69	87
No. of Students	15	34	37	44	12

The correct answer is 49.

To find the mean of a discrete frequency distribution, we use the formula:

$\stackrel{-}{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

where:
• $x_i$ represents the marks value.
• $f_i$ represents the number of students (frequency).

Step 1: Calculate the total number of students ($\sum f_i$)

$\sum f_i=15+34+37+44+12=142$

Step 2: Calculate the product of marks and number of students ($f_i{x}_i$) for each column
• 10 × 15 = 150
• 28 × 34 = 952
• 48 × 37 = 1776
• 69 × 44 = 3036
• 87 × 12 = 1044

Step 3: Calculate the sum of all products ($\sum f_i{x}_i$)

$\sum f_i{x}_i=150+952+1776+3036+1044=6958$

Step 4: Compute the mean

$\text{Mean}=\frac{6958}{142}$

$\text{Mean}=49$

Thus, the mean of the distribution is 49.