a.We will attempt to answer the question "What is the average height of RCCC male students?" using data we collected the first week of this semester. Be sure to give explanations in context and include units when appropriate.

Height (inches)

70, 70, 70, 70, 71, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 68, 69, 72, 72, 72, 72, 73, 73, 73, 73, 73, 73, 74, 75, 75, 75

Describe the population of interest? __________________________________________________

A sample of ________ (state the number) RCCC male students was taken.

We found the sample mean _______ (symbol) to be __________ (2 decimal places). Interpretation: In the sample of male RCCC students, the _______________ (don't use the word "mean") height was approximately ________ inches.

The median is ________ . Interpretation (use the one for mean as a guide):

________________________________________________________________

________________________________________________________________.

The mode is ________ . Interpretation (use the one for mean as a guide):

________________________________________________________________

________________________________________________________________.

b.We know the measures of central tendency don't tell us the whole story, so we then investigated the measures of variation as well. We found that the heights had a range of ___________ with a standard deviation _______ (symbol) of ___________ (2 decimal places) and a variance _______ (symbol) of ___________ (2 decimal places).

1.Chebyshev's Theorem

Note: You will need to use the sample mean and standard deviation from #1.

a.(10 pts) According to Chebyshev's Theorem, at least _______________ % of any dataset lies within 2 standard deviations of the mean. For our sample of heights, this would be between the values __________and___________ (2 decimal places). Show your work!

Mark the two values above on the number line in the dot plot.

From the dot plot, we see that _____ of the 31 men in the sample had heights that fell within 2 standard deviations of the mean, which would be approximately _____ % (0 decimal places).

b.(8 pts) According to Chebyshev's Theorem, at least _______________ % of any dataset lies within 3 standard deviations of the mean. For our sample of heights, this would be between the values__________and___________ (2 decimal places). Show your work!

Using the dot plot, we see that _____ of the 31 men in the sample had heights that fell within 3 standard deviations of the mean, which would be approximately _____ % (0 decimal places).

c.(4 pts) Answer the following question:Did our sample of male heights meet the requirements set forth by Chebyshev's Theorem? ________ Explain.