Question

Find the mean of the numbers \[ 5^2,\;6^2,\;7^2,\;8^2,\;9^2,\;10^2. \]

• A. \(59\dfrac{1}{6}\)
• B. \(60\dfrac{1}{6}\)
• C. \(61\dfrac{1}{6}\)
• D. \(62\dfrac{1}{6}\)

Hint:

Arithmetic mean is given by \[ \boxed{ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} } \] Always evaluate the terms first before calculating the average.

Answer 1

The Correct Option is A

Step 1: Evaluate the squares. \[ 5^2=25,\; 6^2=36,\; 7^2=49,\; 8^2=64,\; 9^2=81,\; 10^2=100. \]

Step 2: Find the sum. \[ 25+36+49+64+81+100=355. \] There are \[ 6 \] numbers.

Step 3: Calculate the mean. \[ \text{Mean} = \frac{355}{6} = 59\dfrac{1}{6}. \]

Step 4: Final conclusion. \[ \boxed{59\dfrac{1}{6}} \] Hence, the correct option is \(\boxed{(A)}\).