Question

Find Variance and coefficient of variance of following data 1 ,2,3,4,5,6,7
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Answer 1

Answer:

0

Explanation:

there us no variable for 1, 2, 3, 4, 5, 6, 7

there are only coefficient

ex. 1 is a coefficient

Answer 2

Answer - The variance is 4.67 and coefficient of variance is 54%.

step by step explaination -The variance of a set of data is a measure of the spread of the data around the mean. It is calculated by taking the average of the squared differences of each data point from the mean.

The formula for variance is:

$variance = \frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}$

To calculate the variance of the data set 1, 2, 3, 4, 5, 6, 7:

First find the mean of the data set: (1+2+3+4+5+6+7)/7 = 4

Next, subtract the mean from each data point and square the result:

$(1-4)^2 = 9 , (2-4)^2 = 4 , (3-4)^2 = 1 , (4-4)^2 = 0 , (5-4)^2 = 1 , (6-4)^2 = 4 , (7-4)^2 = 9$

Sum these squared differences: 9+4+1+0+1+4+9 = 28

Divide this sum by the number of data points (n-1 = 6) to find the variance: 28/6 = 4.67

Coefficient of variance (CV) is a normalized measure of the variation of a random variable with respect to its mean. It is defined as the ratio of the standard deviation to the mean. It is a unitless number and is often expressed as a percentage.

The formula for coefficient of variance is:

$CV = \frac{standard deviation}{mean} * 100%$

To calculate the coefficient of variance of the data set 1, 2, 3, 4, 5, 6, 7:

First, find the standard deviation using the variance: $sqrt(variance) =$sqrt(4.67) = $2.16$

Next, divide the standard deviation by the mean: 2.16/4 = 0.54

Finally, multiply this ratio by 100% to express it as a percentage: $0.54*100%$ = 54%

So the variance is 4.67 and coefficient of variance is 54%.

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