Assume that n distinct values x1,x2,...,xn 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 \(\displaystyle\sum^{8}_{i=1}f_i=\)
- 35
- 45
- 48
- 42
- 40
The Correct Option is B
Solution and Explanation
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
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