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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

  1. A 23.5
  2. B 21.5
  3. C 31.5
  4. D 27
Verified Solution

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…