Statistics

1
StatisticsChapter 5

• Measures of Central Tendency
• Reading Assignment p. 158-161, 163-174, 177-186

2
Measures of central tendency

• Mean, median modehelp to find patterns in data
• Article, p.158
• Univariateapply to one variable at a time
• Give general idea of what respondents are like

3
Mode

• Tells which category of a variable is chosen most
  frequently by respondents
• Category chosen by the most respondents, not
  most of the respondents (pitfalls, p. 163)
• P. 161work status in the GSS

4
Mode (cont.) 2

• There can be more than one mode
• Skills practice 1, p. 164

5
Median 3

• The value that divides the respondents in half
• Arrange items in numerical order (small to large)
• If of items is odd, median is the middle item
• If of items is even, median is the mean of the
  two middles
• Fig. 5.1 and 5.2, p. 165-66

6
Median 3

• To find median case (N1)X 0.5
• Also, can read where cumulative is 50 that is
  where median will occur
• Hank Aaron
  Cumulative Percent
• 32.00 1 4.3 43.5
• 34.00 2 8.7 52.2
• 38.00 1 4.3 56.5

7
Median 3

• When median falls between two values (see table
  5.5, p, 170)
• Pitfalls p. 171

8
4 Mean

• Average
• Article, p. 173
• P. 175, skills practice 3
• Mean of data arranged in a frequency
  distribution for the sum, multiply each score by
  its frequency of occurrence
• Ex, p. 176

9
Characteristics of mean, median , and mode

• Mode and medianleast changed by the unusually
  low or high extreme scores in a data set
• See table, top of p. 180
• When reporting the mean, consider the range to
  see whether the mean is being affected by extreme
  scores.
• Aaron

10
Affect on inferences

• Mean is the most stable of the three measures,
  i.e., if several random samples are taken from
  the same data set, there will be less variability
  among the means than among the medians or modes.
• Table 2, p. 180 table 3, p. 181

11
Normal distributions

• When the shape of the histogram of the
  distribution is perfectly bell-shaped (unimodal
  and symmetricalsingle mode and as many cases
  above the mean as below)
• Skewed distribution in which there are more
  cases below the mean than above it (positive
  skew) or more cases above it than below it
  (negative skew)
• Pitfalls, p. 184
• P. 186summary of central

12
Chapter 5 homework

• P. 189/ 1,5,15, (not hand in)
• Hand in p. 189/ 11
• SPSS P. 194/ 1,3