# Descriptive Statistics

How do you determine how the data is normaly distributed?

How do you determine the standard deviation from the mean?

What are the steps to determine the tons of coffee that a population will export?

1. Use the features of the Normal Distribution to answer the following questions about coffee:

Below is a copy of an Excel file with data on 80 coffee roasters across the world. These data represent the number of tons of coffee exported during the year 2004.

8.5 8.56 8.59 8.61 8.63 8.65 8.66 8.68

8.51 8.56 8.59 8.61 8.63 8.65 8.66 8.69

8.52 8.57 8.59 8.62 8.63 8.65 8.66 8.69

8.53 8.57 8.6 8.62 8.64 8.65 8.66 8.69

8.54 8.57 8.6 8.62 8.64 8.65 8.66 8.69

8.54 8.57 8.61 8.62 8.64 8.65 8.66 8.7

8.54 8.58 8.61 8.62 8.64 8.65 8.67 8.71

8.54 8.58 8.61 8.62 8.64 8.65 8.67 8.72

8.55 8.58 8.61 8.63 8.64 8.66 8.67 8.73

8.56 8.59 8.61 8.63 8.65 8.66 8.67 8.75

Descriptive statistics from Microsoft Excel are below.

0.25 range

8.623375 mean

8.63 median

8.65 mode

-0.19779 skew

0.052215 Stdev

o Given the evidence reviewed above, are the data normally distributed? Why or why not?

IMPORTANT! Use the descriptive statistics to argue that the data are, or aren't normally distributed. Share your rationale: On what basis do you declare that the data are, or aren't normally distributed? Remember that in your reserved reading and in our lecture notes, you learned six techniques for determining whether data are normally distributed. Be sure that your rationale includes no less than two of those techniques.

o Assuming the data are normally distributed, we could expect what percentage of the population of coffee roasters across the world to export between the mean and +2 standard deviations from the mean?

o Assuming the data are normally distributed, we could expect 68% of the population of coffee roasters across the world to export approximately how many tons of coffee? (i.e. between what "low" number and what "high" number?)

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#### Solution Summary

The solution provides step by step method for the calculation of descriptive Statistics . Formula for the calculation and Interpretations of the results are also included.