Descriptive Statistics Essay

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Assignment

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(32 points due by 11 pm October 14th)

1) The file ‘FastFood’ contains the amount that a sample of nine customers spent for lunch (in $) at a fast food restaurant.

a) Compute the mean and the median.
b) Compute the variance, standard deviation, range, and co-efficient of variation. c) Are the data skewed? If so, how?

2) The file ‘ChocolateChip’ contains the cost (in cents) per 1 ounce serving, for a sample of 13 chocolate chip cookies.

a) Compute the first quartile, the third quartile, and the interquartile range. b) Construct a boxplot and describe its shape.

3) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the 50 states and the District of Columbia during a recent year.

a) Compute the mean, variance, and standard deviation for the population.

Mean= 12,999
Variance=15,258,895
Standard deviation=3906.26

b) What proportion of these states has per capita energy consumption within + or – 1 standard deviation of the mean, within + or – 2 standard deviations
of the mean, and within + or – 3 standard deviations of the mean?

There are 11 within +-1, 12 within +-2, and 26 within +-3.

c) Compare your findings with what would be expected based on the empirical rule.

Compared to the empirical rule I would say my data agrees with it. My first standard deviation got the least my second standard deviation got the 2nd most and my third standard deviation had the rest.

d) Repeat a) through c) with the District of Columbia removed. Have the results changed?
Da.mean=12,857, varience = 14,549,046, standard deviation = 3,814.32
Db. There are 11 within +-1, 12 within +-2, and 25 within +-3.
Dc. The data is still exactly the same as before, when it comes to comparing it to the empirical rule, except it lost one within the +-3 standard deviation.

4) The file ‘Cereals’ lists the calories and sugar (disregard carbohydrates) in grams, in one serving of seven breakfast cereals.

a) Compute the covariance.
Cereal
Calories (x)
Sugar (Y)
(X-X avg)(Y-Yavg)
Kellogg All Bran
80
6
7.15
Kellogg Corn Flakes
100
2
115.71
Wheaties
100
4
55.71
Nature’s Path Organic Multigrain Flakes
110
4
37.14
Kellogg Rice Krispies
130
4
0

Post Shredded Wheat Vanilla Almond
190
11
308.58
Kellogg Mini Wheats
200
10
290.01
Average
130
5.857
116.328

b) Compute the coefficient of correlation.
Standard deviation of x= 46.9, standard deviation of Y= 3.4
Correlation= (SQRT46.9)x(SQRT3.4)= (6.848)(1.843)=12.6209
Correlation =116.328/12.621
Correlation= 9.217

c) Which do you think is more valuable in expressing the relationship between calories and sugar – the covariance of the coefficient of correlation? Explain.

I think the covariance is more valuable in expressing the relationship between calories and sugar because it is a measure of how much two variables change together and that’s what we are looking at with the sugar and calories.

d) Based on a) and b), what conclusions can you reach about the relationship between calories and sugar?

Judging from A and B the conclusion I can reach about the relationship between calories and sugar is on average for every 9 calories there is one sugar.

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