Question

find the variance of 0,3,2,1,3,5,4,3,42,1,2,,0​

Answer 1

Given:

Following observation is 0,3,2,1,3,5,4,3,42,1,2,0.

To find:

Variance

Solution:

firstly, we have to calculate the mean of the following observations.

for calculation of mean-

$Mean(x) = \frac{\sum n_i}{N}$

∑$n_i$ = sum of all observation

N = no. of total observation

so, we get,

$Mean(x) = \frac{0+3+2+1+3+5+4+3+42+1+2+0}{12}$

Mean = 5.5

Now, calculate standard deviation and for that we have to calculate deviation first.

The difference between every observation to the mean of the given data is known as deviation.

Formula used to calculate standard deviation-

$SD = \sqrt{\frac{\sum D^2}{N}}$

here, D = deviation

∑D² can be calculated as

∑D² = (0-5.5)² + (3-5.5)² + (2-5.5)² + (1-5.5)² + (3-5.5)² + (5-5.5)² + (4-5.5)²                         + (3-5.5)² + (42-5.5)² + (1-5.5)² + (2-5.5)² + (0-5.5)²

∑D² = 1479

SO,

$SD = \sqrt{\frac{1479}{12}}$

SD = 11.101

Now, find the Variance,

Variance = SD²

Variance = (11.101)²

Variance = 123.23

so variance of the following observation is 123.23.