PADM 7060 Quantitative Methods for Public Administration – Unit 2 Spring 2006 Jerry Merwin

PADM 7060 Quantitative Methods for Public Administration – Unit 2

Spring 2006Jerry Merwin

Meier, Brudney & BohtePart II: Descriptive Statistics

Chapter 4: Frequency Distributions Chapter 5: Measures of Central

Tendency Chapter 6: Measures of Dispersion

Meier, Brudney & Bohte: Chapter 4 Frequency Distributions

Descriptive statistics: what are they? How are the following related:

Data Raw data Frequency distributions See Table 4.1 – Arrests per Police Officer

Be sure you know the following: Variable, class, class boundaries, class

midpoints, class intervals, class frequency, total frequency

Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 2)

Be sure you know the following: variable class class boundaries class midpoints class intervals class frequency total frequency


How is a “Frequency Distribution” constructed? Step 1 Step 2 Step 3

Tips: Note tips on page 60 See table 4.2

What is a continuous variable?


What is a percentage distribution? See Tables 4.3 & 4.4 to see how

comparison plays a role. What is a cumulative frequency

distribution? See Table 4.5 Cumulative percentage distribution

See Table 4.6


How are “Graphic Presentations” important? (See Table 4.7 on page 64)

What is a “Frequency Polygon” and how is it done? See pages 63-65 for steps. See figures 4.1, 4.2, & 4.3 Pay attention to the note at the bottom

of page 65.


What is a histogram and under what conditions is it used? (See Table 4.8 on page 66)

See pages 67 for steps. See figures 4.4, 4.5, 4.6, & 4.7


Summary Problems 4.2, 4.4, 4.10

Meier, Brudney & Bohte Chapter 5: Measures of Central Tendency

What are measures of central tendency? Some examples:

Average starting salary of MPA graduates What is the average number of MPA graduates

per year who accepted job offers in nonprofit organizations?

What was the middle score on the midterm? What is the average number of employees who

report job-related accidents every month?

Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 2)

What are the three types of average most often calculated and used? (75)

What is the mean? See formula on page 76. Remember the symbols we saw at the

first of the book? µ is a Greek letter pronounced “mu” and

symbolizes the population mean. ∑ is symbol for summation of all values X N is number of items summed.


More on the mean… See Table 5.1 on page 76.

What are the important characteristics of the mean? (See page 77)

What is an outlier? What did you get for the mean in the

example?


What is the median? (See page 69)

Let’s see an example: the city planning office example on pages 78-79

Note the characteristics on page 79 Not affected by extreme values All observations used to determine, but not all

calculated. Only good measure of central tendency if

values cluster near median Usually not unrealistic value The 50th percentile in distribution of data (GRE)


Explain the “Mode” as a measure of central tendency. See Table 5.2 (*unimodal), 5.3 (bimodal), 5.4 Important characteristics:

Mode is not necessarily near middle of data. Can take on more than one value, so might be

best summary of central tendency with bimodal or trimodal and other complex distributions. (Note: Mean might hide something important about data in these cases.)

With less precise measures, nominal and ordinal, mode is useful. Not so in interval scales.


How do we get the means for grouped data? Ideally we use raw data, but might not

have it in every situation. Archival and “sensitive survey” data

require grouped data. (Discuss sensitive)

We lose information (frequencies, etc.) with grouped data, so statistics are less accurate.


How do we get the means for grouped data? (Continued)

Example: Oklahoma Highway Department data in Table 5.5 How did the analyst calculate the mean?

(data grouped by classes or categories) See steps on pages 82-83 Table 5.6 with midpoints for each class Table 5.7 with (∑ F x M) /N

Serious Crimes per Precinct in Metro, TX Table 5.8


How do we get the means for grouped data? (Continued)

Serious Crimes per Precinct in Metro, TX Table 5.8 How are these data different? What does the difference mean about the

calculation? Evanapolis Recreation Department

Letters of thanks received by employees Table 5.9


What about “Medians” for grouped data? See steps on pages 84-85 Table 5.10


What is the “Crude Mode” for grouped data? See 86 The midpoint of the class with the

greatest frequency.


How do we determine when the Median might be better measure of central tendency for numerical data than the mean? Outliers (Have we talked about this before?)

Skewed – means? Example: housing prices More to come in Chapter 6


How are levels of measurement and measures of central tendency related? See pages 86-90 Tables 5.11-5.15

What is the “Hierarchy of Measurement” used in chapter 5? See table 5.16 on page 90


What cautions are provided regarding the levels of measurement and coding of response categories? See page 91 Note Table 5.17

How can we avoid ordinal-interval debate?


Summary Problems 5.2, 5.16

Meier, Brudney & Bohte Chapter 6: Measures of Dispersion

What do we mean by a measure of dispersion? See Table 6.1 & Figure 6.1 on page 100

What are some measures of dispersion?

Meier, Brudney & Bohte Chapter 6: Measures of Dispersion (Page 2)

What is standard deviation? See Table 6.2, 6.3, & 6.4 Steps begin on page 101 Formula for σ of population on page 102

How is the standard deviation for a sample (s) calculated differently?


How is the standard deviation for grouped data calculated? See Table 6.5 Steps are on page 104


What is the importance of the shape of a frequency distribution? See Figure 6.2 for a symmetric

distribution Figure 6.3 for uniform distribution Figure 6.4 for a bimodal distribution Figure 6.5 for a negatively skewed

distribution Figure 6.6 for a positively skewed

distribution


What is the importance of the shape of a frequency distribution? See Figure 6.2 for a symmetric

distribution Figure 6.3 for uniform distribution Figure 6.4 for a bimodal distribution Figure 6.5 for a negatively skewed

distribution Figure 6.6 for a positively skewed

distribution


Why do we need to use the measures of dispersion and measures of central tendency together? See page 108

Meier & Brudney: Chapter 6 Measures of Dispersion (Page 7)

Summary Problems 6.2, 6.4, 6.8

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PADM 7060 Quantitative Methods for Public Administration – Unit 2 Spring 2006 Jerry Merwin