The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f₁ and f₂:

To find the missing frequencies \( f_1 \) and \( f_2 \) in a frequency distribution where the mean is given, we can use the formula for the mean of a frequency distribution:

Mean Formula

The mean (\( \bar{x} \)) is calculated as:

\( \bar{x} = \frac{\sum (f \cdot x)}{\sum f} \)

Where:

• \( f \) = frequency
• \( x \) = midpoint of the class interval

Given Values

From the problem, we know:

• Mean (\( \bar{x} \)) = 62.8
• Sum of frequencies (\( \sum f \)) = 50

Setting Up the Equation

Let’s denote the total sum of \( f \cdot x \) as \( S \). The equation becomes:

\( 62.8 = \frac{S}{50} \)

From this, we can find \( S \):

\( S = 62.8 \times 50 = 3140 \)

Finding Missing Frequencies

If we have two missing frequencies \( f_1 \) and \( f_2 \), we can express the total sum of frequencies as:

\( f_1 + f_2 + \text{(other frequencies)} = 50 \)

And the total sum of \( f \cdot x \) as:

\( f_1 \cdot x_1 + f_2 \cdot x_2 + \text{(other products)} = 3140 \)

Solving the System

To find \( f_1 \) and \( f_2 \), you will need additional information about the class intervals or the values of \( x_1 \) and \( x_2 \). Once you have those, you can set up a system of equations to solve for the missing frequencies.

In summary, use the mean formula to find the total sum of \( f \cdot x \) and set up equations based on the known frequencies to solve for \( f_1 \) and \( f_2 \).