Question

Question: The Insurance Institute for Highway Safety publishes data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The cost for a sample of 9 cars, in hundreds of dollars, is provided below: 10,6,8,10,4,3.5, 7.5,8,9. (a) What is the median cost of the total damage suffered for this sample of cars? (b) What is the first quartile for the above data? (C) What is the interquartile range of the above data? (d) What is the mean of the total damage suffered for this sample of cars? (e) Using the correct units, what is the value of the variance?

Answer 1

collection & The given data are 10, 6, 8, 10, 4, 3.5, 7.5, 8, 9 no Firstly, the data are arranged in ascending order, as, Ascending order : 3.5, 4, 6, 7,5,8,8, 9, 10, 10 a) median = value of 10th) t observation if nis odd. value of ith observation sth observation = = value of 8 Median b) first quartile 19 ) = value of th obste hobservation. value of = value of (2.5th observation value of and obs" + 0,5(value of 3rd. absha value of and obsng = A + 0.51 6-4) = 4 +0.5x2 9 - 5 2 .8 cmedian Third quartile (93) = value of $3/2+19th observations & value of [3 / 3+15th obs" = value of (7.85th obsn = value of thosht os[value of 8th obs" - 7th obs] = 9+0.5 [10-9]

c) Inter quartile Range (I.Q.R) - = = 93-91 9.5- 5 4.5 ) Mean - Sum of All observations (Toral No. of obsn 7-33 mean - 733 le vastance . = Elxi-x) 2. that X;- ) 14486689 16.0899 1.76 0.0289 0.81489 0.4499 2.7889 7.1989 7.1989 Variance at 45. soll - 5.6876 in Hundred of dollarsque Variance = 5.6876 dollars