Chapter 2 Descriptive Statistics: Tabular and Graphical Methods

Transcription

1 Chapter Descriptive Statistics Page of 7 /7/9 Chapter Descriptive Statistics: Tabular and Graphical Methods Data can be classified as either qualitative data, names or labels for groups of data, or quantitative data that uses some measuring device to assign a value to each observation. Summarizing Qualitative Data: The methods of summarizing qualitative data is to count the membership and/or to find the proportion in each category or group and to present the data in tabular form or a chart. The tabular presentation of the data is known as a frequency distribution showing counts in each category. One example would be to summarize the state license plates where travelers or visitors cars are registered A B C D E F G H I Ohio Michigan Michigan State Frequency Proportion Cumulative Michigan Iowa Iowa Michigan.7.7 Iowa Ohio Ohio Iowa 9.5. Ohio Indiana Wisconsin Ohio..9 Indiana Illinois Indiana Indiana.7. Illinois Indiana Ohio Illinois..9 Iowa Michigan Iowa Wisconsin.. Michigan Iowa Ohio. Iowa Michigan Iowa Ohio Iowa Ohio Wisconsin Ohio Indiana Ohio Indiana Illinois In the above worksheet use the excel countif( ) worksheet function to count the occurrences of the state name in the list of state names. You can double click on cell F to see the function (=COUNTIF($A$:$C$,E)) used to count the occurrences known as the frequency. The proportion, also called the relative frequency, column computes the proportion which is the frequency divided by the total and again double click on cell G to see the formula (=F/$F$). The "$" symbol used in the formula lock or freezes the cell row and/or column reference. A column chart or pie chart of the above state license plate data is created by graphing the frequency or relative frequency (proportion) data.

2 Chapter Descriptive Statistics Page of 7 /7/9 Michigan Iow a Ohio Indiana Illinois Wisconsin A pie chart displaying the same data would use the same frequency and label columns and show the relative frequency or proportion to the total as follows. Michigan Iow a Ohio Indiana Illinois Wisconsin One additional graph type is called an Ogive that displays the cumulative frequencies or cumulative relative frequencies is illustrated below.

3 Chapter Descriptive Statistics Page of 7 /7/ Michigan Iow a Ohio Indiana Illinois Wisconsin Summarizing Quantitative Data Quantitative data needs to be distributed over groups that have specific beginning and ending points for each group or class in a process called classifying data. The first task is to determine the number of classes and the width (beginning and ending value) of each group or class. A useful formula, displayed below, is to determine the exponent value on a base of is greater than the number of observations in the sample. The exponent value is the number of classes to use. I will generally tell you how many classes to use. c > n i = r c

4 Chapter Descriptive Statistics Page of 7 /7/ A B C D E F MPG Data Class At Least Less Than Frequency Stem and leaf displays have an advantage in that the individual data values are preserved and not lost when the other display methods are used. The number 9 is placed in the tens row and the 9 value is the leaf. The number is tens and one so on the stem row place a. Multivariate Data: To this point we have addressed one variable data sets. Some statistical problems involve two or more variables in a set of data. Consider the following data set Study Time (hours spent studying per credit hour) and GPA, TV Time (hours watched per credit hour) and GPA, and Shoe Size and GPA.

5 Chapter Descriptive Statistics Page 5 of 7 /7/ A B C D E F G H I Study Time GPA TV Time GPA Shoe size GPA Positive or Direct Relationship The following graph will show the relationship between Study Time and GPA. Intuitively one might suspect that the relationship is positive or direct indicating the more you study the higher your GPA. Conversely, the less you study the lower your GPA Negative or Inverse Relationship: The chart showing the relationship between TV Time per credit hour is shown next. One might expect that as the TV time along the X-axis increases the lower the GPA will fall. The television time is the X-

6 Chapter Descriptive Statistics Page of 7 /7/9 Axis data and the GPA is the Y Axis. By adding a trend line excel also places the equation of the line of best fit known as the trend line on the graph and the value of R squared that indicated the strength of the relationship. The r-squared value range extends from, indicating no relationship to, a strong relationship No correlation: One final graph of the relationship between shoe size and GPA that would show that two sets of data are not related.

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