Question

The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed (in grams) and recorded in the table below. Hershey claims that there is 368 grams of chocolate in one bag.

4.76	4.72	4.74	4.55	4.91	4.74	4.78	4.71	4.8
4.78	4.78	4.75	4.79	4.82	4.91	4.83	4.68	4.74
4.7	4.8	4.7	4.76	4.7	4.83	4.93	4.74	4.84
4.82	4.78	4.77	4.72	4.78	4.83	4.75	4.74	4.68
4.84	4.71	4.71	4.76	4.66	4.78	4.73	4.74	4.92
4.77	4.8	4.79	4.86	4.64	4.78	4.7	4.75	4.78
4.76	4.83	4.66	4.77	4.83	4.78	4.69	4.81	4.68
4.78	4.88	4.72	4.85	4.85	4.81	4.74	4.8	4.82
4.84	4.7	4.85	4.7	4.81	4.72	4.79	4.63

To help you answer the questions below use your scientific calculator. Your scientific calculator is capable of doing calculations on entire data sets by first entering the data and then pressing combinations of keys to find the average and standard deviation etc... You should check with your calculator manual to see how this special data handling feature works. Let the instructor know if you have any questions. You will need to learn how to do this for testing purposes. Note: Instructions for several brands of calculators in included in the folder Course Overview/Excel & Calculator Instructions.

1. What is the Mean and Median? (you may want to use your calculator!)

2. In general, each Kiss® is approximately how many grams? Explain what measure you used and why.

3. What is the Range? Are you surprised at this? Why or why not?

4. What could be some reasons for variation in the weights of the Kisses®? NOTE: Take time answering this one. There are lots of thingsto consider here and I'll be looking for a well thought out answer with several given reasons contributing to the variation. Of course, the wrappers and tags could vary but what about the drops of chocolate themselves? Why aren't they all the same?

5. Would you say that there are any two Kisses that could have exactly the same weight? (I mean exactly the same weight!)

6. How many Kisses® were there in the bag?

7. Based on Hersheys® claim for 368 total net grams of chocolate in the bag, approximately how many Kisses® too many or too few are there? Give some possible explanations for this difference.

8. EXCEL: Click on and print out one of the following: Excel Descriptive Statistics 2016/2013 to see how to enter the Kiss data into a worksheet and obtain a list of descriptive statistics and a histogram with no more than 12 classes. Also, make sure to sort your data using the Sort command under Data on the menu bar. Submit your Excel file to the Lab1 Part 1 Dropbox.

9. Standard Deviation & Empirical Rule: Variation is a big factor in the analysis of most any data set and it will be very important to have a way of measuring it. Standard Deviation is one such measure that you will study and learn to calculate in an upcoming section. For now, find the Standard Deviation number on your Descriptive Statistics read-out from Excel. There is a rule for "mound-shaped" distributions that can help you have some feeling for what this standard deviation number is telling you. It's called the Empirical Rule and is stated below:
For any data set having a bell-shaped (or mound-shaped) distribution the following are true:
- Approximately 68% of the data values will be within one standard deviation of the mean.
- Approximately 95% of the data values will be within two standard deviation of the mean.
- Almost all of the data values will be within three standard deviation of the mean.
Use the standard deviation value given in Excel and the Empirical Rule (stated above) to find answers to the following:
a) Find the percentage of all the Kisses in the bag that fell within 1 standard deviation of the mean? ... within 2?, … within 3?
(Show how you calculated these percentages!)
b) How close is the Empirical Rule in predicting the percentages that you calculated above?
c) If your calculated percentages did not line up with the percentages claimed by the Empirical Rule, speculate on some possible reasons for this.

10. How might standard deviation and the shape of the distribution indicate how consistent Hershey® is in the manufacturing of their Kisses®?

PART 2 - Data Collection & Discussion

Task 1: Answer the following Questions

In Lab 1 Part 1 you have constructed a Histogram for the Hershey Kisses by using Excel. Think about the following questions then answer them thoroughly.

Would you consider the distribution of the weights to be roughly mound-shaped? Why or why not?

Is the shape of the distribution what you might have expected? Why or why not?
(In other words, give a non-technical explanation as to why you might have thought that the weights from a bag of Hershey Kisses would produce a mound-shaped histogram.)
If you answered 'no' to this question, explain why you should have expected it to be mound-shaped.

Do you think that Hershey^® collects and analyzes the same kind of data we have collected thus far? Why? Of what value could this be to them?

Task 2: Collect your own data!

The mound shaped distribution is a very common distribution. Find something other than Kisses^® to collect data on that would produce a mound-shaped distribution. Also, don't use weights nor candy, make it something totally different than the Hershey Kisses. Follow the steps below.

Step 1) Think of other things you could collect data on that might produce a mound-shaped distribution (histogram). There are lots of possibilities here and there are lots of other measurements besides weight such as quantity, length, time, dollars, etc ... .
You shouldn't have to do anything that costs you money!

Step 2) Collect data on this.

Step 3) Do an analysis similar to what was done with the Hershey Kisses^®. In other words, Put your data into Excel, get a Descriptive Statistics output and create a histogram. Instructions for Excel are located in the Excel & Calculator Instructions folder under Course Overview.

Step 4) Put together a small report that explains what the data was taken from and how you collected it.

Make sure to upload the answers to all the questions in Task 1, Excel file (with data, descriptive statistics, histogram) and report from Task 2 to the Lab 1 Part 2 Dropbox located in this folder. Actually you can just put everything into one Excel file and upload it!

Answer 1

1) Mean= 4.7685 g

Median= 4.775 g

2) In general, each kisses is approximately 4.7685 g. We use generally, the mean to indicate approximate weight of each chocolate. Mean is the measure of central tendency to establish a common behavior among variables.

3)Range of the chocolate is 0.38g. I am surprised because the range is quite too high for a given mean. It is almost 10% of the mean weight.

4) There may be difference in viscosity of chocolate from time to time, when it is highly liquified, more amount of chocolate drop would have happened, and hence may be the result in variation along with wrappers and tags differences.

5) The given data consists of a lot of chocolates with exactly the same weight. This can be calculated by finding mode which gives the value, which is repeated most number of times. Hence, from the analysis, most of the chocolates in the sample has a weight of 4.78g

6) There were 80 kisses in the bag

7)The total weight was 381.48g and given weight is 368 g, hence extra weight divided by average weight of kisses give extra chocolates, which is 3 in this case.