Question

The ages at death for a sample of 40 residents who died in certain city are listed below. 25 35 43 65 47 77 54 94 81 57 72 62 83 44 66 92 78 69 71 82 59 73 63 76 89 48 69 79 56 98 80 82 74 85 77 68 93 55 97 72 The inter-quartile range, IQR, for the given data is 23 24 23.5 O 24.5

Answer 1

Let write data in order

25   35   43   44   47   48   54   55   56   57

59   62   63   65   66   68   69   69   71   72

72  73   74   76   77   77   78   79   80   81

82  82   83   85   89   92   93   94   97   98

1st Quartile is given as..

$Q_1=\frac{n+1}{4}=\frac{40+1}{4}=\frac{41}{4}=10.25$

10.25th Observation =10th Obs + 0.25( 11th Obs - 10th Obs )

10.25th Observation =57+0.25(59-57)= 57.5

$\framebox{Q_1=57.5}$

$Q_3=\frac{3(n+1)}{4}=\frac{3(40+1)}{4}=\frac{123}{4}=30.75$

30th Observation =30th Obs + 0.75( 31th Obs - 30th Obs )

10.25th Observation =81+0.75(82-81)= 81.75

$\framebox{Q_3=81.75}$

$\framebox{Inter\: Quartile\: range=24.25}$