Statistics—Chapter 5 Measures of Central Tendency Reading Assignment: p , ,

Measures of central tendency Mean, median mode—help to find patterns in data Article, p.158 Univariate—apply to one variable at a time Give general idea of what respondents are like

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. 161—work status in the GSS

Mode (cont.) 2 There can be more than one mode Skills practice 1, p. 164

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

Median 3 To find median case: (N+1)X 0.5 Also, can read where cumulative % is 50; that is where median will occur Hank Aaron Cumulative Percent

Median 3 When median falls between two values (see table 5.5, p, 170) Pitfalls p. 171

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

Characteristics of mean, median, and mode Mode and median—least 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

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

Normal distributions When the shape of the histogram of the distribution is perfectly bell-shaped (unimodal and symmetrical—single 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. 186—summary of central

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