# lecture4note(1) - Psych 100A Measures of variation Lecture...

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1 Lecture 4: Descriptive Statistics: Psych 100A Numerical summaries of data: Measures of variation 1 Measures of variation a. Range. Difference between the largest and the smallest measurements in a data set. Range = max – min. b. Interquartile range (IQR). Difference between the upper and lower quartiles. IQR = 75 th percentile (Q3) – 25 th percentile (Q1). 2 Calculating Percentiles (not in text) p th percentile – is a value such that no more than p% of the data is less than this value and no more than (100-p)% of the data is greater than this value. If np/100 is an integer, the average of the values corresponding to the [np/100]th and [(np/100)+1]th ordered observations. The k th ordered observation if np/100 is not an integer, where k is the smallest/closest integer greater than np/100. 3 Note: Percentiles can be calculated in different ways and they may give different correct answers. You will get credit for any valid method, but I recommend using the method described above. Example The following data represents cotinine levels in saliva (nmol/l) after smoking. We want to compute the 20th percentile.