# Question: 7 let x1 xn be a...

###### Question details

*7. Let {x1, . . . , xn} be a data set of real numbers and let yi = axi + b, for i = 1, . . . , n, for some a 6= 0. (a) Let x = 1 n Pn i=1 xi and s 2 x = 1 n−1 Pn i=1(xi−x) 2 . Show that y = ax+b and s 2 y = a 2 s 2 x . (b) Find expressions for the median, interquartile range and trimmed mean of {yi} in terms of those of {xi}. (Note: why do you need to consider the cases a > 0 and a < 0 separately?) (c) Let x denote temperature in degrees centigrade and let y denote temperature in degrees Fahrenheit, so y = 1.8x+ 32. Assume the {xi} data set has mean 68.1, median 68.9, variance 3.2 and IQR 7.7. Calculate the corresponding quantities for the {yi} data.