PSY302
Chapter 2: Central tendency and variability
Psychological Statistics
Robert Lockamyeir
Central Tendency
Summarizes a group of scores (a distribution) with a single number
Most “typical” or common score to represent the distribution as a whole
Measures of central tendency:
Mode
Median
Mean
Mode
Most frequently occurring number in a distribution
Mode of dataset: 7,8,8,7,3,1,6,9,3,8 = 8
With large datasets, make a frequency table and find the value or category with the most responses (highest frequency)
Used as a measure of central tendency for nominal (categorical) variables
Median
The middle score when scores are organized from lowest to highest
Line up all the scores from lowest to highest
Figure how many scores there are to the middle score by adding 1 to the total number of scores (N) and dividing by 2
Median Position (MP) = (N+1)/2
Count up to the middle score or scores. If you have one middle score, this is the median. If you have two middle scores, the median is the average (the mean) of these two scores
Median
Most appropriate as a measure of central tendency for rank-ordered (ordinal) variables
Examples:
11,12,13,14,15
11,12,13,14
Mean
The average, the sum of all scores divided by the total number of scores
Most appropriate as a measure of central tendency for equal-interval variables
Σ = “sum of”; add up all scores following this symbol
Χ = scores in the distribution
N = total number of scores in the distribution
Mean
Advantages
Most common measure of central tendency because all scores in a distribution are included in its calculation
Useful in many statistical procedures because there are going to be many different responses
Disadvantages
Susceptible to extreme scores, called outliers
A score that is very different from the majority of scores can significantly change the mean
Comparing Mean, Median, and Mode
In a normal distribution, the mean, median and mode are all the same
In skewed distributions, the mean is “pulled” toward the tail of the distribution
In a positively skewed distribution, the median is lower (smaller) than the mean
In a negatively skewed distribution, the median is higher (larger) than the mean
Comparing Mean, Median, and Mode
Measures of Variability: Variance
A distribution can be characterized by how much the scores in it vary from each other
Variance is the average of the squared deviation scores from the mean
Deviation score: score (X) minus the mean (M)
Sum of squares (SS): the sum of the squared deviations from the mean
Measures of Variability: Variance
Measures of Variability: Variance
Steps for computing the variance:
Each score (X) minus the mean (M)
Square each of these deviation scores: (X-M)2
Add up the squared deviation scores: Σ(X-M)2
Divide the sum of squared deviation by the number of scores
Measures of Variability: Standard Deviation
Most common way of describing the spread of a group of scores
Standard deviation is the average amount that scores differ from the mean (above or below)
Measures of Variability: Standard Deviation
Steps for computing the standard deviation:
Figure the variance
Take the square root
Lab Problems
Pg. 60-61: 1abcde, 2abcde