chapter 1

Chapter 1: Overview and Descriptive StatisticsSupplementary Exercises62. To somewhat simplify the algebra, begin by subtracting 76,000 from the original data. Thistransformation will affect each date value and the mean. It will not affect the standarddeviation.x1= 683,x2= 1,048, y = 831n x =( 4)(831) = 3,324 so, x + x + x + x 3, 3241 2 3 4=2+ x3= 3,324− x1− x4= 1, xx and = ( 1,− x )and 5932Next, s = ( 180)2⎡⎢= ⎢⎢⎢⎣∑So, 2 =2,859, 444x2x i−( 3324)342⎤⎥⎥⎥⎥⎦2 2 2 2∑ i1+ x2+ x3+ x4=2 22 22+ x3= 2,859,444 − x1+ x4= 1,294,6513593x , 2,859, 444By substituting x3 ( 1593−x 2)22+ ( 1,593 − x ) −1,294,65102 2=2x x−1,593x2+ 621,499 = 0x and= we obtain the equationx .x we obtain x2=682. 8635 and x3= 1,593−682.8635=910. 1365 .2763=Evaluating for2Thus, x = ,683 x 76, 910 .231