Quantitative data types
 Expressed numerically, and ordered on a scale
 Interval data: increase at constant intervals, but do not start at zero, eg. temperature on the Celsius scale
 Ratio data: interval data which has a true zero, eg. pressure
 Binary data: yes or no answers
 Discrete data: isolated data points separated by gaps
 Continuous data: part of a continuous range of values
This sort of data is described by measures of central tendency, dispersion, and "shape".
 This is the average of a population  allowing the population to be represented by a single value.
 Examples: Median, mode (value which occurs most frequently) and the means (arithmetic mean and geometric mean)
 These describe the dispersion of data around some sort of mean.
 Range: the highest and the lowest score
 Percentile: the percentage band into which the score falls (mean = the 50th percentile)
 Deviation: distance between an observed score and the mean score
 Variance: deviation squared
 Standard deviation: square root of variance
 Measure of the average spread of individual samples from the mean
 Reporting the SD along with the mean gives one the impression of how valid that mean value actually is (i.e. if the SD is huge, the mean is totally invalid  it is not an accurate measure of central tendency, because the data is so widely scattered.)
 Standard error
 This is an estimate of spread of samples around the population mean.
 You dont known the population mean you only know the sample mean and the standard deviation for your sample, but if the standard deviation is large, the sample mean may be rather far from the population mean. How far is it? The SE can estimate this.
Standard Error (SE) = SD / square root of n




 The variability among sample means will be increased if there is (a) a wide variability of individual data and (b) small samples
 SE is used to calculate the confidence interval.
Shape of the data
 This vaguely refers to the shape of the probability distribution bell curve.
 Skewness is a measure of the assymetry of the probability distribution  the tendency of the bell curve to be assymmetrical.
 Kurtosis or "peakedness" describes the width and height of the peak of the bell curve, i.e. the tendency for the scores to gather around the middle of the bell curve.
 A normal distribution is a perfectly symmetrical bell curve, and is not skewed.