Example 1. The following scores were given by 6 judges for a gymnast's performance in the vault of an international meet : 7, 5, 9, 7, 8, and 6. Find the range, variance, and the standard deviation of this population. Solution N=6 Range=9-5=4 7+5+9+7+8+6_:42_ M: 6 6 -7.0 E(X '7)2 (7'7)2+(5'7)2+(9'7)2+(7'7)2+(8'7)2+(6'7)2 02 : i=1 6 6 =23 6 = 1.6667 7 1.67 5 6 7 7 8 9 Q3 : 8 Q1=6 0= 1.6667 = 1.29 QD=Q3-Ql) : (8 - 6)/2 = 1 2 Variance: 52 = E i? - 7? Standard deviation, 8 = \\f7 n-1