Chapter 2 The Mean, Variance, Standard Deviation, and Z Scores

Measures of Central Tendency The Mean  Sum of all the scores divided by the number of scores  Mean of 7,8,8,7,3,1,6,9,3,8 –ΣX = = 60 –N = 10 –Mean = 60/10 = 6

Measures of Central Tendency The Mode  Most common single number in a distribution  Mode of 7,8,8,7,3,1,6,9,3,8 = 8  Measure of central tendency for nominal variables

Measures of Central Tendency The Median  The middle score when all scores are arranged from lowest to highest  Median of 7,8,8,7,3,1,6,9,3,8 – median –Median is the average (mean) of the 5 th and 6 th scores, so the median is 7

Measures of Spread The Variance  The average of each score’s squared difference from the mean  Steps for computing the variance: 1. Subtract the mean from each score 2. Square each of these deviation scores 3. Add up the squared deviation scores 4. Divide the sum of squared deviation scores by the number of scores

Measures of Spread The Variance  Formula for the variance:

Measures of Spread The Standard Deviation  Most common way of describing the spread of a group of scores  Steps for computing the standard deviation: 1. Figure the variance 2. Take the square root

Measures of Spread The Standard Deviation  Formula for the standard deviation:

Z Scores  Number of standard deviations a score is above or below the mean  Formula to change a raw score to a Z score:

Z Scores  Formula to change a Z score to a raw score:  Distribution of Z scores –Mean = 0 –Standard deviation = 1

Controversies and Limitations The Tyranny of the Mean  Knowledge about the individual case is lost when taking averages  Qualitative research methods –e.g., case studies, ethnography

The Mean and Standard Deviation in Research Articles  Commonly reported in research articles