#### If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m+n is equal to _____. Option: 1 12 Option: 2 18 Option: 3 16 Option: 4 20

Dispersion (Variance and Standard Deviation) -

Variance and Standard Deviation

The mean of the squares of the deviations from the mean is called the variance and is denoted by σ2 (read as sigma square).

Variance is a quantity which leads to a proper measure of dispersion.

The variance of n observations x1 , x2 ,..., xn is given by

Standard Deviation

The standard deviation is a number that measures how far data values are from their mean.

The positive square-root of the variance is called standard deviation. The standard deviation, usually denoted by σ  and it is given by

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variance of the first n natural numbers is 10

n = 1,2,3,4........n

Using variance formula

variance of the first m even natural numbers is 16

N = 2,4,6,8........2m

N = 2(1,2,3,4........m)

Using variance formula

Hence