Question

The mean of the following distribution is 23.8 .

\[ \begin{array}{|c|c|c|c|c|c|} \hline \textbf{Class} & 0\text{–}10 & 10\text{–}20 & 20\text{–}30 & 30\text{–}40 & 40\text{–}50 \\ \hline \textbf{Frequency} & 7 & 5 & 3 & 4 & k \\ \hline \end{array} \]

What is the value of \( k \)?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

For frequency distributions, always use the midpoint of each class and the given mean formula.

Answer 1

The Correct Option is B

The mean \( \bar{X} \) of a frequency distribution is given by: \[ \bar{X} = \frac{\sum f x}{\sum f} \] where \( f \) is the frequency and \( x \) is the class midpoint. For the given classes, the midpoints are: 0–10: \( 5 \), 10–20: \( 15 \), 20–30: \( 25 \), 30–40: \( 35 \), 40–50: \( 45 \). Using the formula: \[ 23.8 = \frac{7(5) + 5(15) + 3(25) + 4(35) + k(45)}{7 + 5 + 3 + 4 + k} \] Simplifying and solving for \( k \), we get \( k = 6 \).