Download Statistics of Soups

Statistics Project For this assignment, you will implement a project involving statistical procedures. You
will be expected to analyze, interpret, and evaluate information using appropriate technological tools. The
topic may be something that is related to your work, a hobby, or something you found interesting. If you
choose, you may use the example described below. The project report must include name of project and
your name purpose of project data (provide the raw data used, and cite the source)—the sample size must
be at least 10 median, sample mean, range, sample variance, and sample standard deviation (show work)
frequency distribution histogram percentage of data within one standard deviation of the mean, percentage
of data within two standard deviations of the mean, percentage of data within three standard deviations of
the mean (include explanation and interpretation --- do your percentages imply that the histogram is
approximately bell-shaped?) conclusion (several paragraphs interpreting your statistics and graphs; relate to
the purpose of the project) If you choose, you may use the following example for your data. Purpose:
Compare the amount of sugar in a standard serving size of different brands of cereal. (You may instead
choose to compare the amount of fat, protein, salt, or any other category in cereal or some other food.)
Procedure: Go to the grocery store (or your pantry) and pick at least 10 different brands of cereal. (Instead
of choosing a random sample, you might purposely pick from both the "healthy" cereal types and the
"sugary" ones.) From the cereal box, record the suggested serving size and the amount of sugar per serving.
The raw data is the serving size and amount of sugar per serving for each of the 10 boxes of cereal. Before
calculating the statistics on the amount of sugar in each cereal, be sure you are comparing the same serving
size. If you use a serving size of 50 grams, you must calculate how much sugar is in 50 grams of each
cereal. For example, if the box states that there are 9 grams of sugar in 43 grams of cereal, there would be
50 times 9 divided by 43, or 10.5 grams in 50 grams of cereal. The result of this simple calculation (for
each of 10 boxes) is the data you will use in the project statistics and charts.
Salt in Soups – a comparison of some popular types and brands
By ________________________
For this comparison study, we selected 12 soups from a local grocery store and recorded the amount of salt
(i.e. sodium) in each. The raw data are listed in the table below.
Brand/Type
Sodium/cup
cups/can
Sodium/can
Healthy Choice Minestrone
360
2
720
Campbell's Condensed Tomato Soup
(Healthy Request)
410
2.5
1025
Campbell's Condensed Tomato Soup
480
2.5
1200
Campbell's Condensed Cream of
Mushroom
650
2
1300
Campbell's Select Harvest 100%
Natural Harvest Tomato with Basil
650
2
1300
Progresso Traditional 99% Fat-free
Chicken Noodle
670
2
1340
Progresso Rich and Hearty Steak and
Vegetables
690
2
1380
Progresso Vegetable Classics Garden
Vegetable
690
2
1380
Campbell's Condensed Cream of
Broccoli
750
2.5
1875
Progresso Traditional 99% Fat-free
New England Clam Chowder
810
2
1620
870
2.5
2175
880
2.5
2200
Campbell’s Chunky Beef with
Country Vegetables
Campbell’s condensed Manhattan
Clam Chowder
Note that the serving size is 1 cup (8 oz) for all entries in this table. We will compute all of our statistics
using the sodium per cup values. The basic descriptive statistics are given in the table below:
Statistic
Maximum
Minimum
Value
880
360
Mean
659.2
Median
Standard Deviation (σ)
167.9
% within 1σ
67%
% within 2σ
100%
% within 3σ
100%
680
The mean (average) is found by summing all the values and dividing by 12 (the number of samples). The
median is the middle value of the sorted list, and since we have an even number of samples, we take the
average of the two nearest the middle (samples 6 and 7). The standard deviation is the square root of the
average deviation from the mean. The maximum and minimum are self-explanatory. All of these
calculations were done with Excel. The percentages of the data within 1, 2 and 3 standard deviations were
simply counted by hand.
The histogram or frequency distribution of the data is shown below. From this we see the data are roughly
bell-shaped, but are slightly skewed to the low-sodium side.
7
number of soups
6
5
4
3
2
1
0
0
200
400
600
800
sodium per cup
1000
1200