Question

Descriptive Statistics and Graphical Displays

Valencia Orange Price Comparison

You have been hired as a consultant to determine who ABC Grocery Store should be ordering Valencia Oranges from.

To: Statistician

From: ABC Grocery Store

Please advise us on which company to use as our orange distributor. Three highly recommended distributors have provided us with statistical data on the weekly prices for one load of Valencia oranges per week for a ten-week period last year. Prices fluctuate according to availability, and we would like to use the company with the lowest overall price and the least amount of fluctuation. We would like your written report showing your results and a detailed recommendation as to which company we should choose.

Thank you.

Here are the prices, listed as price in dollars per crate:

Week	The Fruit Guys	Sunny Oranges	Tree Groves
1	350	345	345
2	350	295	340
3	310	325	310
4	330	315	290
5	340	290	305
6	290	305	290
7	305	300	320
8	315	315	320
9	325	340	300
10	355	350	359

You must type in and analyze the data for each company.

Helpful directions:

1. Analyze the data for each company: frequency, relative frequency, mean, median,******* (ONLY complete the mode, standard deviation and range because below I am going to list my answers for the frequency, relative frequency, mean and median)
2. You need to decide which statistics to compare to determine the overall lowest price and the least fluctuation. Create and include at least two charts that will be useful to best support your conclusions.
3. Write a brief informative letter in response to the request from ABC Grocery answering their request. Be sure to include:
   1. A very detailed explanation of the data and the conclusions you came to. You should use the statistics you calculated to make this decision.
   2. Charts to support your explanation.
4. Attach copies of the Excel pages or embed the Excel work in your letter of response.

Answer 1

The descriptive statistic is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2:DATA > Data Analysis > Descriptive Statistic > OK. The screenshot is shown below,

Step 3: Select Input Range: All the column, tick on the Summary statistic. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

From the result summary,

	The Fruit Guys	Sunny Oranges	Tree Groves
Mean	327	318	317.9
Median	327.5	315	315
Mode	350	315	290
Standard Deviation	21.8835	21.3698	23.6335
Range	65	60	69
Minimum	290	290	290
Maximum	355	350	359

From the summary statistics, we can see that Sunny Orange and Tree Groves have the lowest mean and median value while among these two Sunny Orange has a lower standard deviation.

Now, to see that the shape of the distribution, a histogram is obtained for each orange distributor in the following steps,

The Fruit Guys

Step 1: Write the data values in excel.

Step 2: Let the number of classes = 5

Now, the classes are,

Class

290-303

304-316

317-329

330-342

343-355

Step 3: Make a column bin with an upper limit of class interval then

DATA > Data Analysis > Histogram > OK. The screenshot is shown below,

Step 4: Insert Input Range: The Fruit Guys column, Bin Range: bin column then OK. The screenshot is shown below,

The frequencies are obtained.

Class	Frequency
290-303	1
304-316	3
317-329	1
330-342	2
343-355	2

Similarly, the histograms are obtained for the other two distributors. The screenshots are shown below,

For Sunny Oranges

Bin	Frequency
302	3
314	1
326	3
338	0
350	2

For Tree Groves

Bin	Frequency
304	3
318	2
332	2
346	2
360	0

From the three histograms, we can see that the Sunny Oranges is least varied and more values towards the lower prices