Question

If the mean of the distribution is \(5\), then the value of \(P\) is:

\[ \begin{array}{|c|c|c|c|c|c|} \hline x_i & 2 & 4 & 6 & P & 10 \\ \hline f_i & 3 & 2 & 1 & 4 & 2 \\ \hline \end{array} \]
 

• A. \(7\)
• B. \(5\)
• C. \(8\)
• D. \(4\)

Hint:

For a discrete frequency distribution, \[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i}. \] First compute \(\sum f_i x_i\), then substitute the given mean to find the unknown value.

Answer 1

The Correct Option is B

Step 1: Calculate \(\sum f_i x_i\). \[ \sum f_i x_i = (3\times2)+(2\times4)+(1\times6)+(4\times P)+(2\times10) \] \[ = 6+8+6+4P+20 = 40+4P. \]

Step 2: Calculate total frequency. \[ \sum f_i = 3+2+1+4+2 = 12. \]

Step 3: Use the given mean. \[ 5 = \frac{40+4P}{12}. \] \[ 60=40+4P. \] \[ 20=4P. \] \[ P=5. \] Therefore, \[ {P=5}. \]