The table given below shows the number of pens owned by each student in a class.

| No. of pens | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| No. of students | 6 | 2 | 9 | 9 | r | 2 | 2 |

If the mean is 2.5, find the value of r?

To find the value of r , the number of students owning 4 pens, we start by using the formula for the mean (average):
Mean = Total number of values Sum of all values ​
In this context, the 'values' are the number of pens, and their frequency is the number of students. The mean is given as 2.5.
First, calculate the total number of students:
6 + 2 + 9 + 9 + r + 2 + 2 = 30 + r
Now, calculate the total number of pens:
( 0 × 6 ) + ( 1 × 2 ) + ( 2 × 9 ) + ( 3 × 9 ) + ( 4 × r ) + ( 5 × 2 ) + ( 6 × 2 )
This simplifies to:
0 + 2 + 18 + 27 + 4 r + 10 + 12 = 69 + 4 r
Use the mean formula:
Mean = 30 + r 69 + 4 r ​ = 2.5
To find r , cross-multiply to remove the fraction:
69 + 4 r = 2.5 × ( 30 + r )
Distribute 2.5:
69 + 4 r = 75 + 2.5 r
Subtract 2.5 r from both sides:
69 + 1.5 r = 75
Subtract 69 from both sides:
1.5 r = 6
Divide by 1.5:
r = 4
So, the value of r is 4. This means there are 4 students who own 4 pens each.

Answered by DanielJosephParker | 2025-07-06