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Further3 summarising univariate data

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Further3 summarising univariate data

1. 1. Further MathematicsSummarising univariate data K McMullen 2012
2. 2. Summarising Univariate DataMeasures of Centre Mean: the arithmetical average of all the individual values in a set of values Sum of all data values/number of data values Median: the middle value is an ordered data set Mode: the most frequently occurring value in a data setOutliers: extreme values that don’t fit in with the dataset The mean is affected by outliers whereas the mode and median aren’t The median is the best measure of centre when you are working with skewed data or data that contains outliers (eg. House prices) K McMullen 2012
3. 3. Summarising univariate dataRange: The difference between the largest andsmallest value MAX value minus MIN value Is affected by outliersInterquartile range (IQR): represents the spreadof the middle 50% IQR= Upper quartile (Q3) minus Lower quartile (Q1) Upper quartile: The middle of the upper half Lower quartile: The middle of the lower half K McMullen 2012
4. 4. Summarising Univariate DataStandard Deviation (s): measures the spread ofthe distribution of data around the mean Easily calculated using CAS Used when dealing with normal distributionsThe range, IQR and standard deviation allmeasure the spread of data The larger the spread the more varied the data set is K McMullen 2012
5. 5. Summarising Univariate DataFive number summary: the five number issummary identifies the important components ofa box plot The summary must be stated in this order: Minimum value Lower quartile Median Upper quartile Maximum All 5 of these components must be displayed on a box plot K McMullen 2012