MHT CET · Maths · Statistics
If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations is
- A 30
- B 51
- C 50
- D 31
Answer & Solution
Correct Answer
(D) 31
Step-by-step Solution
Detailed explanation
Let the observations be
\(x_1, x_{2,}, x_3, \ldots x_{50}\)
Then, \(\sum_{i=1}^{50}\left(x_i-30\right)=50\)
\(\begin{aligned}
& \Rightarrow \sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}-(30 \times 50)=50 \\
& \Rightarrow \sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}=1550
\end{aligned}\)
\(\text {Mean }=\frac{\sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}}{\mathrm{n}}=\frac{1550}{50}=31\)
\(x_1, x_{2,}, x_3, \ldots x_{50}\)
Then, \(\sum_{i=1}^{50}\left(x_i-30\right)=50\)
\(\begin{aligned}
& \Rightarrow \sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}-(30 \times 50)=50 \\
& \Rightarrow \sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}=1550
\end{aligned}\)
\(\text {Mean }=\frac{\sum_{\mathrm{i}=1}^{50} x_{\mathrm{i}}}{\mathrm{n}}=\frac{1550}{50}=31\)
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