Question

The mean of the following data \(21^2,22^2,\ldots,30^2\) is

• A. 678.5
• B. 668.5
• C. 658.5
• D. 648.5

Hint:

To find the mean: \[ \boxed{\text{Mean}=\frac{\text{Sum of all observations}}{\text{Number of observations}}.} \] Always count the number of observations carefully.

Answer 1

The Correct Option is C

Concept: The mean is given by \[ \boxed{\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}.} \] Here the observations are \[ 21^2,22^2,\ldots,30^2. \] There are \[ 30-21+1=10 \] observations.

Step 1: Find the sum of the squares.
\[ \begin{aligned} 21^2+22^2+\cdots+30^2 &=441+484+529+576+625 &\quad+676+729+784+841+900 &=6585. \end{aligned} \]

Step 2: Calculate the mean.
\[ \text{Mean} =\frac{6585}{10} =658.5. \]

Step 3: Final conclusion.
Hence, \[ \boxed{658.5} \] is the required mean.