 Social statistics  Descriptive statistics  Inferential statistics  Mean, median and mode Z519--Spring 2015

 Range  Variance  Standard deviation  Using Excel and SPSS to calculate them

 Descriptive statistics  Centrality tendency (average)  Measurement of variability (variability)  Average+Variability = describe the characteristics of a set of data

 Variability  How scores differ from one another  Three sets of data  7, 6, 3, 3, 1  3, 4, 4, 5, 4  4, 4, 4, 4, 4  Variability = the difference from the mean

 Three ways  Range  Variance  Standard deviation

 The most general measure of variability  How far apart scores are from one another Range = highest score – lowest score What is the range for the follow numbers? 98, 86, 77, 56, 48

 Variance  The average of the squared deviations from the mean

 Standard deviation (SD)  Average deviation from the mean (average distance from the mean)  Represents the average amount of variability

 The right figure shows 2013 GDP per Capita for select countries-- current US$  Please calculate the variance and standard deviation by hand or by using excel (VAR.S() & STDEV.S()) Data collected from CountryGDP per Capita Afghanistan678 Brazil11208 Canada51958 Chile15732 Greece21910 Japan38492 Lebanon9928 Norway Panama11037 Saudi Arabia25852 Singapore55182 Tunisia4329 United States53143 Vietnam1911 Zimbabwe905

STDEV.S STDEV.P VAR.S VAR.P

 STDEV.S is standard deviation for sample (biased SD)  STDEV.P is standard deviation for population (unbiased SD)  If your dataset is the whole population, use STDEV.P to calculate standard deviation  If you dataset is the sample of something, use STDEV.S to calculate standard deviation

 To be conservative  STDEV  This is the standard deviation for sample  Take n-1 in order to make STDEV a bit larger than it would be.  If we have error, we compensate by overestimating the STDEV

Sample sizeNumerator in standard deviation formula Denominator Population standard deviation STDEV.P (dividing by n) Denominator Sample standard deviation STDEV.S (dividing by n-1) Difference between STDEVP and STDEV

 Often appears in the “Results” sections of journals  They are quite different  Variance is squared SD

mean SD = 1.76 Variance = 3.1 Average distance to mean=( )/10=1.4

 Standard Deviation (SD) = the average distance from the mean  The larger SD, the more different data are from one another  Since mean is sensitive to extreme scores, so do SD  If SD=0, this means that there is no variability in the set of scores (they are all identical in value) – this happens very rarely.

 Average life expectancy for females in is reported for 10 countries. Please calculate the range, variance and SD for European counties, Non- European countries, and all countries.

 You and your friends have just measured the heights of your dogs (in millimeters):  The heights (in mm) (at the shoulders) are: 600, 470, 170, 430 and 300.  Find out the Mean, the Variance, and the Standard Deviation.

Western Airlines Flight Report ThursdayFridayThursdayFridayThursdayFriday Morning FlightsTo Kansas To Philadelphia To Providence Number of passengers ThursdayFridayThursdayFridayThursdayFriday Evening FlightsTo Kansas To Philadelphia To Providence Number of passengers

 Write a half page summary report to your boss  Form a group to discuss it