TS EAMCET · Maths · Statistics
The standard deviation of \(a, a+d, a+2 d, \ldots, a+2 n d\) is
- A \(n d\)
- B \(n^2 d\)
- C \(\sqrt{\frac{n(n+1)}{3}} d\)
- D \(\sqrt{\frac{n(n+3)}{3}} d\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{n(n+1)}{3}} d\)
Step-by-step Solution
Detailed explanation
Given series, \[ a, a+d, a+2 d, \ldots, a+2 n d \] Here, \(\quad a+2 n d=a+(m-1) d\) \[ \begin{array}{rlrl} \Rightarrow & & 2 n d=(m-1) d \\ \Rightarrow & 2 n=m-1 \\ \Rightarrow & & 2 n+1=m \end{array} \]…
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