final statistics exam 21 aug 14

Benjamin A. Manuel Elementary Statistics August 21, 2014

Final Exam

Statistics Book Raw Data

Statistics Class Raw Data

Objectives

1) Gather data from three brands of chocolate chip cookies.See page 1

2) Create charts and gather information using the data from the in class testing and as displayed in the Elementary Statistics book, 12th edition.See pages 2 and 3

3) Create a box plot with the data.See page 3

4) Create a Histogram with the data.See pages 4 through 6

5) What brand of cookie gets you the most chocolate chips for the money?See page 7

6) What were the differences between the data obtained for the Elementary Statistics book and the information obtained through the testing in class?See page 7

7) Identify the mean, standard deviation, median, variance, and range for each set of data.See page 3

8) Identify other statistical calculations that can be performed in order to provide meaningful information about the data obtained.

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Three different brands of cookies were selected for testing. A comparison was drawn from the findings in the Elementary Statistics book and the findings of the testing performed during the final exam. Students chose one brand of cookie to dismantle. Due to the amount of cookies to dismantle and the time available, the choice was made to collect a sample of 1/3 the total number of each type of cookie. There were 33 Chips Ahoy, 24 Keebler, and 24 Always Save cookies. So, 1/3 resulted in randomly selecting 11 Chips Ahoy, 8 Keebler, and 8 Always Save cookies. It is worth noting that the Always Save brand cookies had a significantly smaller size chocolate chip.

The price of each box of cookies was: Chips Ahoy $3.49, Keebler $3.69, and Always Save $1.19.

Information Derived from Raw Data

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Cookie Data Chart

Boxplot

Histogram for Chips Ahoy, Book

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Histogram for Keebler, Book

Histogram for Chips Ahoy, Class

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Histogram for Keebler, Class

Histogram for Always Save, Class

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How much for each chocolate chip?

[(mean per cookie* number of cookies in bag) / price]= Chips per pennyNote: size of chocolate chips and amount of cookies per bag.

Brand Mean/ cookie

Number of Cookies per bag

Chips per bag Price per bag

Chips per penny

Chips Ahoy (b) 23.95 33 790.35 $3.49 2.26Keebler (b) 30.41 24 729.84 $3.69 1.97

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Chips Ahoy 25.18 33 830.94 $3.49 2.38Keebler 26.62 24 638.88 $3.69 1.73Always Save 16.38 24 393.12 $1.19 3.30

Based on the above information, the Always Save brand will give you the most chocolate chips for each penny invested. The Keebler cookie will give you the most chocolate chips per cookie and is the most expensive overall for price per bag, price per cookie, and price per chocolate chip.

Differences from book results to class results

Based on the above information, there are many similarities in the data and there is a glaring difference. Depending on how serious the results of this test were to the information gatherer and/ or their employer, a retest of the information is advisable. Different testing methods could be introduced (test for chocolate chip by weight with a scale). Perhaps a training program that standardizes employee counts of chips or the definition of what is a chip versus a fragment or particle would further refine these results.

Similarities: Keebler has the most chocolate chips per cookie Chips ahoy has less chocolate chips per cookie

Differences: The book results between Keebler and Chips Ahoy were more dramatic than those obtained in

class. In the book, the difference between the mean of Chips Ahoy as opposed to Keebler was 6.46 more for the Keebler cookie. The class testing produced a result of 1.44 more chocolate chips in the Keebler cookie as opposed to the Chips Ahoy cookie.

Dot Plot versus Stem Plot Comparison

The Charts below illustrate the data obtained using a dot plot and a corresponding stem plot. In this case, the stem plot is next to useless as compared to the dot plot. The dot plot also demonstrates that more cookies needed to be tested to supply a more accurate depiction of the number of chips per cookie and more accurate distributions. The data was useful, considering it was compiled within time constraints. However, the data does seem incomplete as compared to the books data.

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Book Results

In Class Test Results

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In Class Test Results, Continued

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References:

Elementary Statistics 12th Edition, Mario F. Triola, copyright 2014

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final statistics exam 21 aug 14

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