Calculating Standard Deviation and Coefficient of Variation

To calculate the standard deviation and coefficient of variation for the given data, follow the steps below:

Step 1: Calculate the Mean
Add all the values in the data and divide by the total number of values to find the mean.
For the given data, the mean is:

(4+5+7+7+8+8+8+9) / 8 = 6.75

Step 2: Calculate the Variance
Subtract the mean from each value, square the result, and add up all the values. Divide this sum by the total number of values minus one to find the variance.
For the given data, the variance is:

((4-6.75)^2 + (5-6.75)^2 + (7-6.75)^2 + (7-6.75)^2 + (8-6.75)^2 + (8-6.75)^2 + (8-6.75)^2 + (9-6.75)^2) / (8-1) = 2.1875

Step 3: Calculate the Standard Deviation
Take the square root of the variance to find the standard deviation.
For the given data, the standard deviation is:

sqrt(2.1875) = 1.479

Step 4: Calculate the Coefficient of Variation
The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage.
For the given data, the coefficient of variation is:

(1.479 / 6.75) x 100% = 21.93%

Conclusion

The standard deviation for the given data is 1.479 and the coefficient of variation is 21.93%. The standard deviation measures the amount of variation or dispersion in the data, while the coefficient of variation is a relative measure of variation that accounts for the size of the mean. A higher coefficient of variation indicates a higher degree of dispersion relative to the mean. In this case, the coefficient of variation is relatively high, indicating a relatively high degree of variation in the data set.