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 scientificcalculator. Your scientific calculator is capable of doingcalculations on entire data sets by first entering the data andthen pressing combinations of keys to find the average and standarddeviation etc... You should check with your calculator manual tosee how this special data handling feature works. Let theinstructor know if you have any questions. You will need to learnhow to do this for testing purposes. Note: Instructions for severalbrands of calculators in included in the folder CourseOverview/Excel & Calculator Instructions.
1. What is the Mean and Median? (you may want to use yourcalculator!)
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 whynot?
4. What could be some reasons for variation in the weights ofthe Kisses®? NOTE: Take time answering this one.There are lots of thingsto consider here and I'll be looking for awell thought out answer with several given reasons contributing tothe variation. Of course, the wrappers and tags could vary but whatabout the drops of chocolate themselves? Why aren't they all thesame?
5. Would you say that there are any two Kisses that could haveexactly 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 chocolatein the bag, approximately how many Kisses® too many or too few arethere? 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 howto enter the Kiss data into a worksheet and obtain a list ofdescriptive statistics and a histogram with no more than 12classes. Also, make sure to sort your data using theSort command underData on the menu bar. Submit your Excelfile to the Lab1 Part 1 Dropbox.
9. Standard Deviation & Empirical Rule:Variation is a big factor in the analysis of most any data set andit will be very important to have a way of measuring it.Standard Deviation is one such measure that youwill study and learn to calculate in an upcoming section. For now,find the Standard Deviation number on yourDescriptive Statistics read-out from Excel. There is a rule for\"mound-shaped\" distributions that can help you have some feelingfor what this standard deviation number is telling you. It's calledthe 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 onestandard deviation of the mean.
- Approximately 95% of the data values will be within two standarddeviation of the mean.
- Almost all of the data values will be within three standarddeviation of the mean.
Use the standard deviation value given in Excel and the EmpiricalRule (stated above) to find answers to the following:
a) Find the percentage of all the Kisses in thebag that fell within 1 standard deviation of the mean? ... within2?, … within 3?
(Show how you calculated these percentages!)
b) How close is the Empirical Rule in predictingthe percentages that you calculated above?
c) If your calculated percentages did not line upwith the percentages claimed by the Empirical Rule, speculate onsome possible reasons for this.
10. How might standard deviation and the shape of thedistribution indicate how consistent Hershey® is in themanufacturing of their Kisses®?
PART 2 - Data Collection & Discussion
Task 1: Answer the following Questions
In Lab 1 Part 1 you have constructed a Histogramfor the Hershey Kisses by using Excel. Think about the followingquestions then answer them thoroughly.
Would you consider the distribution of the weights to be roughlymound-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 youmight have thought that the weights from a bag of Hershey Kisseswould produce a mound-shaped histogram.)
If you answered 'no' to this question, explain why you should haveexpected it to be mound-shaped.
Do you think that Hershey® collects and analyzes thesame kind of data we have collected thus far? Why? Of what valuecould 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 onthat would produce a mound-shaped distribution. Also, don't useweights nor candy, make it something totally different than theHershey Kisses. Follow the steps below.
Step 1) Think of other things you could collectdata on that might produce a mound-shaped distribution (histogram).There are lots of possibilities here and there are lots of othermeasurements 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 donewith the Hershey Kisses®. In other words, Put your datainto Excel, get a Descriptive Statistics output and create ahistogram. Instructions for Excel are located in theExcel & Calculator Instructions folder underCourse Overview.
Step 4) Put together a small report that explainswhat 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) andreport from Task 2 to the Lab 1 Part 2 Dropboxlocated in this folder. Actually you can just put everything intoone Excel file and upload it!
