Question

Consumer Reports (November 1993) surveyed a sample of brands of chicken soup on various nutritional characteristics. Below are their data on calories from fat in one 8-ounce serving. Imagine that the editor has hired you to perform a statistical analysis of how these calories are distributed, and that you will be paid according to the quality of your analysis.

            Calories from Fat in One Serving of Chicken Soup:

            30, 39, 10, 24, 28, 11, 39, 34, 30, 23, 14, 30, 39, 38, 30, 26

Descriptive Statistical Analysis

1. Compute the following quantitative descriptive statistics (leave 2 decimal places in your answers and also include the units of the variable where appropriate):

            Mean               First Quartile                Variance                      Minimum (lowest value)

            Median            Third Quartile              Standard Deviation      Maximum (highest value)

Now you must interpret your specific statistical results. The editor has said that he will pay you only if you describe and explain the meaning of the actual numbers that you calculated. He will not pay you for general definitions that could apply to any example.

2. Which of these statistics are measures of center? What are their values? In this case, which measure of center do you recommend that the editor report as more typical of most soups’ fat calories, and why?

3. What is the shape of this distribution? In what two ways can you tell? What does the shape tell about how the fat calories are distributed (both the majority and the extremes)?

Answer 1

1 calculating mean of the distribution :

_{445/ 16}

_{= 27.81}

_{hence, mean calories from fat in the soup are 27.81 kcal.}

_{2.median: ( first we will order the data in ascending order. Since the frequency is 16, an even number, we will take the mean of the two central values as the median)}

39, 39, 39, 38, 34, 30, 30, 30, 30, 28, 26, 24, 23, 14, 11, 10.

=30+30

2

= 60/2

= 30

Hence, the median is 30. In other words, exactly half the time fat content in the soup are below 30 kcal and exactly half the time they are above 30

3.Maximum value :  is the data value (or values) that has the highest value in the distribution which means that it best represents the upper limit of the average quantity of calories from fat in the soup. The maximum value is 39

4: minimum value: in the given distribution, 10 is the lowest value.

5. The first quartile (Q₁) is defined as the middle number between the smallest number and the median of the data set. Hence, 24 represents the first quartile or 25 per cent of the distribution.

6. The third quartile (Q₃) is the middle value between the median and the highest value of the data set.

Thus, 34 covers 75 per cent of the distribution.