Week 2 Assignment and in both a MS Word document and an Excel document in the same submission.

1.Our weekly discussion scenario about the requested dollar amount for meals includes a spreadsheet full of numbers.  When you are asked to calculate the mean of those numbers, are you calculating a population mean or a sample mean. How do you know?  What does the scenario tell you?

2.  Given these numbers

13, 22, 455, 1, 7, 13, 6, 13, 13, 4, 5, 25, 12, 7

In Excel (include your spreadsheet in your submission):

Calculate the mean:

Calculate the median:

Calculate the mode:

Why was the mean higher than the median or mode?

Why wouldn the mean always be the best number to represent the central tendency of a group of numbers?  Use this example to illustrate your point.

• 3.Calculate the range, variance, and standard deviation in EXCEL for the SAMPLE below.  Then, calculate the range, variance and standard deviation in EXCEL as if the group of numbers was a POPULATION.  Upload your spreadsheet to your submission with the calculations from #2 and #3.
•                  13, 22, 455, 1, 7, 13, 6, 13, 13, 4, 5, 25, 12, 7

Range of the sample:

Range of the population:

Variance of the sample:

Variance of the population:

Standard deviation of the sample:

Standard deviation of the population:

Why did the standard deviation and variance change when you calculated it for the sample and the population for this set of numbers?  What about the formula causes this change?  (Analyze the formulas 7hat is different?)

Go toL

https://www.mathsisfun.com/data/standard-deviation… 

4.   From their website, 

a. Summarize what variance is.

b.  Summarize what standard deviation is.

c.  Look at where they showed the formulas for variance and standard deviation.  What makes these formulas different?

d.  Explain why we need to square distances (scroll all the way down to the Footnote) when calculating variance.

5.Explain the following in your own words: 

percentile, 

the first quartile, 

the third quartile, 

and the IQR (interquartile range). 

Use the list of numbers: 13, 22, 455, 1, 7, 13, 6, 13, 13, 4, 5, 25, 12, 7

to find these values for the data set.  Use the Excel commands that are inclusive in this exercise.  (=quartile.inc)

6.  Go to the internet and find information on the Excel commands =quartile.inc and = quartile.exc

Create a set of at least 6 numbers, and then use your set up numbers to explain the difference between the two commands.

7.   Find the outlier formula that uses the IQR to determine if a number is an outlier. Use the formula to mathematically show that there is an outlier in the data set in #2.

Data set: 13, 22, 455, 1, 7, 13, 6, 13, 13, 4, 5, 25, 12, 7

8. In #2, use the data for the SAMPLE. EXCEPT take out the 455.  Assume the data set is normally distributed, even if it is not.  Use the empirical rule to calculate the range of values that are 1 standard deviation from the mean.  Show your work.  Do the same for two and three standard deviations from the mean. Hint:  This is very similar to what you did in the discussion.