Question

The mean square deviation of a set of observations \(x_1,x_2,\ldots,x_n\) about point \(c\) is defined as \[ \frac1n\sum_{i=1}^n(x_i-c)^2. \] The mean square deviations about \(-2\) and \(2\) are 18 and 10 respectively. The standard deviation of the set of observations is

• A. \(3\)
• B. \(2\)
• C. \(1\)
• D. None of these

Hint:

Use MSD shift formula.

Answer 1

The Correct Option is A

Step 1: \[ \text{MSD}(c)=\sigma^2+(\mu-c)^2 \]
Step 2: \[ \sigma^2+(\mu+2)^2=18 \] \[ \sigma^2+(\mu-2)^2=10 \]
Step 3: Subtracting: \[ 8=8\mu \Rightarrow \mu=1 \]
Step 4: \[ \sigma^2=18-(1+2)^2=9 \Rightarrow \sigma=3 \]