The mean of the following data 12- 22- 32- 42- -2 is1A- nn-12 n-1-6B- 6n-162 n-1-6C- n-12 n-1-6nn-12 n-1-6

The correct option is C The sum of the squares of the first n natural numbers is n(n+1)(2n+1)/6. The mean is the sum divided by the number of terms. Therefore ...

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Standard X

Mathematics

Finding Mean for Grouped Data When Class Intervals Are Not Given

The mean of t...

Question

The mean of the following data $1^{2}, 2^{2}, 3^{2}, 4^{2}, . . . . . . . . n^{2}$ is

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Solution

The correct option is A

The sum of the squares of the first n natural numbers is $\frac{n (n + 1) (2 n + 1)}{6}$ .
The mean is the sum divided by the number of terms. Therefore, the mean is

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

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The mean of the following data 12,22,32,42,........n2 is

The correct option is A The sum of the squares of the first n natural numbers is n(n+1)(2n+1)6. The mean is the sum divided by the number of terms. Therefore, the mean is n(n+1)(2n+1)6n=(n+1)(2n+1)6

The mean of the following data $1^{2}, 2^{2}, 3^{2}, 4^{2}, . . . . . . . . n^{2}$ is

The correct option is A

The sum of the squares of the first n natural numbers is $\frac{n (n + 1) (2 n + 1)}{6}$ .
The mean is the sum divided by the number of terms. Therefore, the mean is

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