Variance and Coefficient of Variation:Using the same data set: 5,8,12,14,18,20,22,255,8,12,14,18,20,22,25,Calculate the variance.Determine the coefficient of variation.

Step 1: Calculate the Mean

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The numbers in the data set are: 5, 8, 12, 14, 18, 20, 22, 25, 5, 8, 12, 14, 18, 20, 22, 25

So, the mean is (5+8+12+14+18+20+22+25+5+8+12+14+18+20+22+25) / 16 = 16

Step 2: Calculate each data point's deviation from the mean

Subtract the mean from each data point to get the deviation of each point.

For example, the deviation of the first data point, 5, is 5 - 16 = -11.

Do this for each data point.

Step 3: Square each deviation

Next, square each deviation. For example, (-11)^2 = 121.

Do this for each deviation.

Step 4: Calculate the Variance

The variance is the average of these squared deviations.

So, add up all the squared deviations and divide by the number of data points.

Step 5: Calculate the Standard Deviation

The standard deviation is the square root of the variance.

Step 6: Calculate the Coefficient of Variation

The coefficient of variation is the standard deviation divided by the mean, often expressed as a percentage.

Note: The above steps are for a sample variance and standard deviation. If your data set is a population, instead of dividing by the number of data points in step 4, you would divide by the number of data points minus 1.