2 7 exploratory data analysis

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This document discusses box and whisker plots and the 5-number summary used to describe data distributions. A box and whisker plot depicts the minimum, lower quartile, median, upper quartile, and maximum of a dataset using a box and whiskers. Outliers are defined as values more than 1.5 times the interquartile range below the first quartile or above the third quartile. The document provides an example comparing temperatures from 2005 and 2008 using a box and whisker plot.

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Two Ways to Characterize Data x i < X – 2s x i > X + 2x x i < Q1 – 1.5  IQR x i > Q3 + 1.5  IQR Outliers Distribution spread, frequency diagram, bar chart and Box and whiskers diagram Picture X and s Minimum, first quartile, median, third quartile, maximum Statistics Mean and standard deviation 5-number summary

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TSTD 6251 Fall 2014 SPSS Exercise and Assignment 1 20 Points In this class, we are going to 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 : Enter the 30 data values in the first column of SPSS Data View Tab Variable View and name this variable receipts Adjust Decimals to 3 decimal points Type Admission Receipts ($ mn) in the Label column for output viewer Return to Data View and click A nalyze on the menu bar Click the second menu D e scriptive Statistics Click F requencies … Move Admission Receipts to the Variable(s) list by clicking the arrow button Click S tatistics … button at the top of the dialog box 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 click all the boxes except for P ercentile(s): and Va l ues are group midpoints . Click Continue to return to the Frequencies dialog box Click OK to generate descriptive statistic output which is pasted below: The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red. Statistics Admission Receipts N Valid 30 Missing 0 Mean 18.76333 Std. Error of Mean 1.278590 Median 17.30000 Mode 19.000 Std. Deviation 7.003127 Variance 49.043782 Skewness 1.734 Std. Error of Skewness .427 Kurtosis 5.160 Std. Error of Kurtosis .833 Range 35.000 Minimum 9.500 Maximum 44.500 Sum 562.900 Percentiles 10 10.61000 20 14.40000 25 15.35000 30 15.50000 40 15.84000 50 17.30000 60 19.00000 70 19.75000 75 22.82500 80 24.10000 90 26.69000 Admission Receipts Frequency Percent Valid Percent Cumulative Percent Valid 9.500 1 3.3 3.3 3.3 9.900 1 3.3 3.3 6.7 10.600 1 3.3 3.3 10.0 10.700 1 3.3 3.3 13.3 11.900 1 3.3 3.3 16.7 14.200 1 3.3 3.3 20.0 15.2.

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8. Two Ways to Characterize Data x i < X – 2s x i > X + 2x x i < Q1 – 1.5  IQR x i > Q3 + 1.5  IQR Outliers Distribution spread, frequency diagram, bar chart and Box and whiskers diagram Picture X and s Minimum, first quartile, median, third quartile, maximum Statistics Mean and standard deviation 5-number summary