There are multiple data sources on the subject you are currently studying - weights of students in college. You’re interested in data that has low variability and a large sample size, the problem is that the data you found isn’t in kilograms but in pounds. Using variance and standard deviation in pounds (1 kg = 2.20462 lb), which data set out of the following would you choose? Measure Data Set A Data Set B Data Set C Sample Size 15 670 4 500 9 334 Mean 550 464 534 Standard Deviation 432 140 210

 Problem    There are multiple data sources on the subject you are currently studying - weights of students in college. You’re interested in data that has low variability and a large sample size, the problem is that the data you found isn’t in kilograms but in pounds. Using variance and standard deviation in pounds (1 kg = 2.20462 lb), which data set out of the following would you choose?

Measure	Data Set A	Data Set B	Data Set C
Sample Size	15 670	4 500	9 334
Mean	550	464	534
Standard Deviation	432	140	210

 Solution 

Here, you were asked to:

• Convert the variance and SD to pounds using the conversion 1 kg = 2.20462 lb
• Choose a data set with low variability and a large sample size

To convert the variance and SD, we simply need to follow the rules for changing units, as seen in the table below.

Measure	Data Set A	Data Set B	Data Set C
Sample Size	15 670	4 500	9 334
Mean
Standard Deviation
CV	79%	30%	39%

To find a preferred data set, you can use the coefficient of variation. Recall that the formula is,

[\

CV = \frac{s}{\bar{x}} *100%

\]

Which tells us the proportion of the standard deviation to the mean. This is what appears in the last row of the table. Because Data Set C has the second lowest variability but almost double the sample size of Data Set B, we’ll choose Data Set C.