Question

The variance of first 5 natural numbers is *​

Answer 1

Answer:

12345

Step-by-step explanation:

first 1

second 2

third 3

4th 4

Answer 2

Given:

The first 5 natural numbers:

1, 2, 3, 4, 5

To Find:

Variance

Solution:

Variance of a number refers to the measure of variability and it showcases the degree of spread in any database.

In simple words, it determines the difference between each number of the set and the set's value of mean.

It can be mathematically summarized using the formula:

S² =  Σ $\frac{(X-m)^{2} }{n}$

where,

m = mean of the set

n = count of numbers in the set  

x = number from the set.

Our set is {1, 2, 3, 4, 5}

Mean value for the set is:

$= \frac{1 + 2 +3 + 4 + 5}{ 5} \\= 3$

Now we know:

m = 10

n = 5

Put the value for every number from 1 to 5 and then see her reaction.

1st

Σ $\frac{{(1 - 3)}^{2} }{5} \\= \frac{4}{5}$

2nd

Σ$\frac{ {(2 - 3)}^{2} }{5} = \frac{1}{5}$

3rd

= Σ $\frac{{(3- 3)}^{2} }{5} = 0$

4th

= Σ $\frac{{(4- 3)}^{2} }{5} = \frac{1}{5}$

5th

= Σ$\frac{{(5- 3)}^{2} }{5} = \frac{4}{5}$

The variance is hence, 0.8 + 0.2 + 0 + o.8 + 0.2

= 2

Hence, the variance of the first five natural numbers is 2.

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