You are a statistician contracted to sample and analyze weights of the 5 lb bags of coffee. You collect the following data:

5.84 5.00 4.48 5.14 5.78 3.98 6.16 6.02 5.52 4.56

4.33 5.63 5.27 4.25 5.43 5.78 4.57 5.03 4.60 5.00

5.82 4.23 5.86 5.22 4.89 5.33 5.53 4.72 5.07 5.60

5.05 5.35 4.28 5.64 5.13 5.56 5.52 5.07 4.30 5.78

4.79 4.89 4.52 4.53 4.52 5.31 5.27 5.22 5.14 5.20

5.03 5.39 5.18 5.19 4.45 5.53 4.96 5.44 5.59 4.60

4.32 4.45 4.91 5.55 5.22 5.65 4.76 5.31 4.39 5.50

6.09 4.52 4.63 5.22 4.51 4.79 5.50 4.98 4.79 4.51

Compute the following statistics using Excel functions so that Excel calculates for you: Mean

Median

First quartile using QUARTILE.EXC

Third quartile using QUARTILE.EXC

Interquartile range (IQR)

Maximum

Minimum

Range

Variance

Standard deviation

Coeficient of Variation (CV)

For the standard deviation, when do you use STDEV.S and when do you use STDEV.P?

Explain why the standard deviation is a better measure to use than the variance.

The coefficient of variation (CV) is a measure of relative variability equal to the ratio between the standard deviation divided by the mean, and formatted to %. It is regularly used to compare risk (volatility) in investing, and is especially useful in to compare data on different scales or with different units of measure. Consider weights of 10 oz, 13.4 oz, 15.1 oz with SD of 2.597 oz. The corresponding weights in pounds 0.625 lb, 0.838 lb, 0.944 lb have SD 0.162 lb. The SDs are not equal, yet the sample and its variability are the same. How can we compare variabilities? The CV, unlike other measures of variability, does not depend on the units of measure. The units are divided out in dividing the standard deviation by the mean. For a "rule of thumb", a CV of greater than 5% is considered significant. So, the CV is also used to assess data with no prior history to compare to evaluate any trends.

When is the Coefficient of Variation (CV) especially useful?

Copy all of the data into cells M1:M80 in order to use Data Analysis Descriptive Statistics.

What happens if you don't and instead use B3:K10 for the Input Range?

Use the Data Analysis, Descriptive Statistics. Click the Summary Statistics box and put the output at B65.

Highlight the mean, median, Standard deviation, Range, Minimum, and Maximum.

As a contracted statistician, you have no prior experience with the company's product. The company has no prior process history and data with which to compare the sample to evaluate any trends.

The mode is not especially useful for this data, but explain why there is or is not a concern with bag weight in terms of the other measures of central tendency.

What statistic should you use to assess variability of the product?

Explain why there is or is not a concern with the variability of the product.