BSB123 Lecture Notes - Lecture 2: Box Plot, Quartile, Summary Statistics
Data Analysis – Numerical Descriptive Measures
- Central Location
oA measure of point around which all scores are centred
oOnly gives a partial picture of the distribution of a set of data i.e. two distribution
may have the same mean but different variability of spread
oMean
Sum of all observations divided by total number of observations
Sample mean –
Population mean –
Difference between sample and population – sample is an estimation of the
population, population is whole
oMedian
Middle value when observations are arranged in ascending order
If n is odd, median is the middle number
If n is even, median is the average of the middle two numbers
oMode
Most frequently occurring observation
Only real measure of central location for qualitative data
Generally grouped and determined using histograms
Modal class used with continuous data
- Dispersion of a Dataset
oMeasure of variation and spread
oLarger variation = greater risk
oVariance
Mean squared deviation from the population mean
Sample variance = sum of all squared deviations/sample size – 1
Population variance = sum of all squared deviations/population
oQuantifying spread of data
Standard Deviation
Distance of each measurement from the mean
Square root of variance
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Document Summary
Sum of all observations divided by total number of observations. Difference between sample and population sample is an estimation of the population, population is whole: median. Middle value when observations are arranged in ascending order. If n is odd, median is the middle number. If n is even, median is the average of the middle two numbers: mode. Only real measure of central location for qualitative data. Dispersion of a dataset: measure of variation and spread, larger variation = greater risk, variance. Mean squared deviation from the population mean. Sample variance = sum of all squared deviations/sample size 1. Population variance = sum of all squared deviations/population: quantifying spread of data. Distance of each measurement from the mean. If the data have a wide spread, the standard deviation will be large: coefficient of variation (cv) Eliminates effect arising from the size of measurements. Measure of shape: skewness of distribution. Mean, median, and mode are in agreement (the same)
