Question

Calculate the standard deviation and coefficient of variation for each data set below, be sure to attach an Excel file to show the work. Explain which of the two mentioned measures can more accurately specify which of these two data sets has more variability or dispersion in their data values, and why.

Data set 1= 11,12,13,14,15,16,17,18,19,20

Data set 2= 8,9,28,29,5,4,1,3,2,10

Answer 1

Dispersion within a dataset can be measured or described in several ways including the range, inter-quartile range and standard deviation

the inter-quartile range is a measure of dispersion that is based upon only two values from the dataset. Statistically, the standard deviation is a more powerful measure of dispersion because it takes into account every value in the dataset.

The range, inter-quartile range and standard deviation are all measures that indicate the amount of variability within a dataset. The range is the simplest measure of variability to calculate but can be misleading if the dataset contains extreme values. The inter-quartile range reduces this problem by considering the variability within the middle 50% of the dataset. The standard deviation is the most robust measure of variability since it takes into account a measure of how every value in the dataset varies from the mean

so data set 2 has more variability of dispersion in terms of high range, IQR and standard deviation.

Fromula:

MEan =AVERAGE(B7:B16)

Standard deviation =STDEV(B7:B16)

Range=MAX(B7:B16)-MIN(B7:B16)

Quartile 1 =QUARTILE(B7:B16,1)

Quartile 3 =QUARTILE(B7:B16,3)

IQR =B21-B20

coeffiecient of variation =(B18/B17)*100

variance=VAR(B7:B16)

Refer above excel file and range for formula reference.