Question

The variance of the series 5, 5, 5, 5,5 is
equal to​

Answer 1

Answer:

0

5

20

25

Answer :

A

Solution :

Given observation are

5,5,5,5,5.

∴ x¯=5+5+5+5+55=255=5

Now, σ2=∑i=15(xi−x¯)2N

Where N = total number of observations.

∴ Variance=σ2

(5−5)+(5−5)+(5−5)+(5−5)+(5−5)5=0

Hence, standard deviation =var−−−√=0

Answer 2

Answer:

The variance of the given series is 0.

Step-by-step explanation:

We know that $\sigma$² = $\sum\frac{x_i-\bar x}{N}$

where  $\sigma$² =  Variance

           $x_i$ = 'i'th term of the series

           $\bar x$ = mean of the series

           N = number of terms in the series

Here,  $\sum$ $\bar x$  = $\frac{5+5+5+5+5}{5}$

                   = $\frac{25}{5}$

                   = 5

          $\sum$ $x_i - \bar x$ = (5 - 5) + (5 - 5) + (5 - 5) + (5 - 5) + (5 -5)

                         = 0

Therefore,  $\sigma$² = $\sum\frac{0}{N}$

                       = 0

Therefore, the variance of the given series is 0.