Probability and Statistics I Chapter 3 Numerical Descriptive Measures Measures of central tendency • Represent a data set by some numerical measures (typical values). • A single value that summarizes a set of data. • It locates the centre of the values. • Give the centre of a histogram or a frequency distribution curve. 3 measures will be considered here : 1. Mean 2. Medi an 3. Mode Measures of central tendency for ungrouped data Mean The mean for popul atio n d ata 1 2 N x ,x ,...,x is denoted by µ and is defined as N 1 2 N i i 1 x x ... x 1 x N N = + + + µ = = ∑ The mean for samp le data 1 2 n x ,x ,...,x is denoted by x and is defined as n 1 2 n i i 1 x x ... x 1 x x n n = + + + = = ∑ Example 3.1 Find the arithmetic mean for the data set { } 15 8, 18 9, 26 5, 12 7, 19 1 . Solution Note 1. Mean not necessary t ak es one o f the valu es i n the o ri gi na l data 2. Mean i s i nf luenc ed by ext reme v al ue Chapter 3 - 1