Central Tendency

Central Tendency statistical measure that accurately describes the center of the distribution and represents the entire distribution of scores. a descriptive statistic

Measures of Central Tendency 80 75 90 95 65 86 97 50 Mean Median Mode

Median 2 5 8 12 14 15 17 19 Middle value, or 50th percentile

Median When there are several scores with the same value in the middle of the distribution Use the following formula: Where: XLRL= lower real limit of the tied values fLRL= frequency of scores with values below XLRL Ftied = frequency for the tied values

Example X f 5 1 4 3 2

Mode Most frequently occurring score in a data set 2 5 8 12 14 15 17 19 Most frequently occurring score in a data set

Reporting Central Tendency in Research Reports In manuscripts and in published research reports, the sample mean is identified with the letter M. There is no standardized notation for reporting the median or the mode. In research situations where several means are obtained for different groups or for different treatment conditions, it is common to present all of the means in a single graph.

Variability

What is Variability?

Measuring Variability the range the standard deviation/variance.

Example 45 39 57 42 54 35 56 41

Variance and Standard Deviation (SD) The most commonly used and most important measure of variability Is the average distance (deviation) between each score in a distribution and the mean of the distribution

Example Score (X) Mean (M) Deviation (X-M) (X-M)2 1 2 3 4

Variance Variance = = Sum of the squared deviations = SS number of scores N = 5.2 5 = 1.04 For samples, variance is computed by dividing the sum of the squared deviations (SS) by n - 1, rather than N (will provide an unbiased estimate of the population variance)

Standard Deviation (SD) M=2.6 SD=0.55 M=2.6 SD=1.82

Computational Formula for SS Score (X) 1 2 3 4