Question

Find the value of \( f \) from the following frequency table if 25 is the mean of marks obtained by the students:

Hint:

To find the missing frequency in a frequency table, use the formula for the mean and substitute the known values to solve for the unknown frequency.

Answer 1

The given data is:

Let the midpoint of each class interval be: \[ \text{Midpoints:} \quad 5, 15, 25, 35, 45. \] Now, calculate the sum of the products of the midpoints and the corresponding frequencies. The formula for the mean is: \[ \text{Mean} = \frac{\sum f x}{\sum f}, \] where \( f \) is the frequency and \( x \) is the midpoint of the class interval. We know the mean is 25, so: \[ 25 = \frac{6 \times 5 + f \times 15 + 6 \times 25 + 10 \times 35 + 5 \times 45}{6 + f + 6 + 10 + 5}. \] Simplify: \[ 25 = \frac{30 + 15f + 150 + 350 + 225}{27 + f}. \] \[ 25 = \frac{755 + 15f}{27 + f}. \] Now multiply both sides by \( 27 + f \): \[ 25(27 + f) = 755 + 15f. \] Simplify: \[ 675 + 25f = 755 + 15f. \] Now, solve for \( f \): \[ 25f - 15f = 755 - 675, \] \[ 10f = 80 \quad \Rightarrow \quad f = 8. \]
Conclusion: The value of \( f \) is 8.