Question

Assume that n distinct values x1,x2,...,x_n occur with frequencies \(f_1,f_2....,f_n\). respectively, If \(\bar{x}=7\) and \(\displaystyle\sum^{8}_{i=1}f_ix_i=315\), then \(\displaystyle\sum^{8}_{i=1}f_i=\)

• A. 35
• B. 45
• C. 48
• D. 42
• E. 40

Answer 1

The Correct Option is B

We are given that \( \bar{x} = 7 \) and \( \sum_{i=1}^{8} f_i x_i = 315 \), and we are asked to find \( \sum_{i=1}^{8} f_i \).

Recall that the mean \( \bar{x} \) is given by:

\[ \bar{x} = \frac{\sum_{i=1}^{8} f_i x_i}{\sum_{i=1}^{8} f_i} \] Substitute the given values into the equation: \[ 7 = \frac{315}{\sum_{i=1}^{8} f_i} \] Solving for \( \sum_{i=1}^{8} f_i \): \[ \sum_{i=1}^{8} f_i = \frac{315}{7} = 45 \]

Answer: 45