Question

For the data 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ......., 9, 9, the product of mean and mode equals

• A. 9
• B. 45
• C. 57
• D. 285

Answer 1

Answer: (C)

57

$1,2,2,3,3,3,4,4,4,4,.....9,9$

As we can see the digits occur according to their value,so

we can say sum$=1^2+2^2+.........+9^2$

Mean$=\frac{1^2+2^2+.........+9^2}{1^2+2^2+.........+9^2}$

Sum of squares of natural number till $n$

$=\frac{n(n+1)(2n+1)}{6}$

Here,$n=9$

$=\frac{\frac{9(9+1)(18+1)}{6}}{45}=\frac{9\times 10\times 19}{6\times 45}$

$=\frac{19}{3}$Mean

As,$9$ is the maximum number and it occurs $9$ times

$\therefore$ mode$=9$

Product of mode and mean $=\frac{19}{3}\times 9=57$

Answer $\left(C\right)$