AP EAMCET · Maths · Statistics
The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10th item of the data, then the variance of the data of ten number is
- A 23.5
- B 21.5
- C 31.5
- D 27
Answer & Solution
Correct Answer
(C) 31.5
Step-by-step Solution
Detailed explanation
\(\because \frac{\sum_{i=1}^9 x_i}{9}=13 \Rightarrow \sum_{i=1}^9 x_i=117\). \(\begin{array}{rlrl} & & & \\ \text { and } & & \sigma^2=25=\frac{\sum_{i=1}^9 x_i^2}{9}-(13)^2 \\ \Rightarrow & \quad \sum_{i=1}^9 x_i^2=9[25+169]\end{array}\) Now, after including…
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