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DMA S1 Key Points – Measures of Location and Spread Raw Data For a set of data values x1 , x2 ,..., xn The mean, x x1 x2 ... x n n x i x or n x i a n a The median is found by arranging the values in order of increasing size. If n is odd, the median is the 21 n 1 th value. If n is even, the median is halfway between the 1 2 n th value and the following value. The mode is the value which occurs with the highest frequency. A data set can have more than one mode if two or more values have the same maximum frequency. A data set has no mode if all the values have the same frequency. The range = largest value – smallest value The interquartile range = upper quartile – lower quartile Q3 Q1 The variance 2 1 2 xi x 2 n The standard deviation is the square root of variance. Grouped Data from Frequency Tables For a data set given in a grouped frequency table, in which the variables takes the value x1 with frequency f1 , x 2 with frequency f 2 and so on. The mean, x x1 f 1 x2 f 2 ... xn f n f 1 f 2 ... f n x f f i i i The median value can be found by drawing a cumulative frequency graph and reading off the value of the variable corresponding to a cumulative frequency equal to half the total frequency. The modal class is the class with the highest frequency density. x f The variance f 2 i i x2 2 i The standard deviation is the square root of variance.