Part II S igma Freud & Descriptive Statistics

Part IISigma Freud & Descriptive Statistics Chapter 2     Means to an End: Computing and Understanding Averages

Measures of Central Tendency • What is Central Tendency? • Three different measures of central tendency… or “averages” • Mean – typical average score • Median – middle score • Mode – most common score

Computing the Mean • Formula for computing the mean • “X bar” is the mean value of the group of scores • “” (sigma) tells you to add together whatever follows it • X is each individual score in the group • The n is the sample size

Things to remember… • N = population size n = sample size • Sample mean is the measure of central tendency that best represents the population mean • Mean is VERY sensitive to extreme scores that can “skew” or distort findings – called “Outliers” • “Average” could refer to mean, median or mode… must specify.

LO1 Example: Car Mileage Case • Sample mean for five car mileages30.8, 31.7, 30.1, 31.6, 32.1 3-5

Computing the Median • Median = point/score at which half of the remaining scores fall below and halffall above. • NO standard formula • Rank order scores from highest to lowest or lowest to highest • Find the “middle” score • BUT… • What if there are two middle scores? • What if the two middle scores are the same?

LO1 Example: Car Mileage Case • Example 3.1: First five observations from Table 3.1:30.8, 31.7, 30.1, 31.6, 32.1 • In order: 30.1, 30.8, 31.6, 31.7, 32.1 • There is an odd so median is one in middle, or 31.6 3-7

Weighted Mean Example • List all values for which the mean is being calculated (list them only once) • List the frequency (number of times) that value appears • Multiply the value by the frequency • Sum all Value x Frequency • Divide by the total Frequency (total n size)

A little about Percentiles… • Percentile points are used to define the percent of cases equal to and below a certain point on a distribution (i.e. data set). • 75th %tile – means that the score received is at or above 75 % of all other scores in the distribution • 25th%tile – means that the score received is at or above 25 % of all other scores in the distribution • “Norm-referenced” measure • allows you to make comparisons

Percentiles and Quartiles For a set of measurements arranged in increasing order, the pth percentile is a value such that p percent of the measurements fall at or below the value and (100-p) percent of the measurements fall at or above the value • The first quartile Q1 is the 25th percentile • The second quartile Q2(median) is the 50th percentile • The third quartile Q3 is the 75th percentile • The interquartile range IQR is Q3 - Q1 3-10

Computing the Mode • Mode = most frequently occurring score • NO formula • List all values in the distribution • Tally the number of times each value occurs • The value occurring the most is the mode Democrats = 90 Republicans = 70 Independents = 140: the MODE!! • When two values occur the same number of times -- Bimodal distribution

When to Use What… • Use the Mode • when the data are categorical (example: # of males vs. females) • Use the Median • when you have extreme scores (outliers) • Use the Mean • when you have data that do not include extreme scores and are not categorical

Using SPSS

Part II S igma Freud & Descriptive Statistics