Discuss the distribution of this set of data by examining kurtosis and skewness

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

In this class, we will study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.

Practice Example:

Admission receipts (in million of dollars) for a recent season are given below for the  n = 30 major league baseball teams:

19.4    26.6    22.9    44.5    24.4    19.0    27.5    19.9    22.8    19.0    16.9    15.2    25.7    19.0    15.5    17.1    15.6    10.6    16.2    15.6    15.4    18.2    15.5    14.2      9.5      9.9

10.7    11.9     26.7   17.5

Require:

a.  Compute the mean, variance and standard deviation.

b.  Find the sample median, first quartile, and third quartile.

c.  Construct a boxplot and interpret the distribution of the data.

d.  Discuss the distribution of this set of data by examining kurtosis and skewness 

     statistics, such as if the distribution is skewed to one side of the distribution, and if the 

     distribution shows a peaked/skinny curve or a spread out/flat curve. 

SPSS Procedures for Computing Summary Statistics:

1. Enter the 30 data values in the first column of SPSS Data View

2. Tab Variable View and name this variable receipts

3. Adjust Decimals to 3 decimal point

4. Type Admission Receipts ($ mn) in the Label column for output viewer

5. Return to Data View and click Analyze on the menu bar

6. Click Descriptive Statistics

7. Click Frequencies …

8. Move Admission Receipts to the Variable(s) list by clicking the arrow button

9. Click Statistics … tap at the top of the dialog box

10. Now, you can select the descriptive statistics according to what the question requires.  For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we select all the boxes except for Percentile(s): and Values are group midpoints (see screenshot).

11. Click Continue to return to the Frequencies dialog box

12. Make sure to Select Display frequency tables to create a frequency table

13. Click OK to generate descriptive statistic output which is pasted below:

The first table (left, below) provides summary statistics of the dataset and the second table (right below) lists frequencies, relative frequencies (percent) and cumulative frequencies. 

 

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