Question

1) a) The following distribution shows the number of cars sold each month by a garage over a period of 3 years: 8 9 10 11 12 13 14 15 Number of cars (x) Number of months (f) 1 4 5 8 5 4 5 4 State whether the variable measured is continuous or discrete and find the mode, the mean and the median. (6 marks) b) The weight (in kg) of 40 patients of the Berkshire Hospital are summarised in the table below. 50 - 60 - 70 - 80 - 90 - Weight in kg (x) 79 99 Number of 13 11 patients (f) 59 100 - 109 69 89 10 3 1 N Estimate the variance and standard deviation for these data. (6 marks) [Total 12 marks]

Answer 1

1) a) The distribution shows the number of cars sold each month by a garage. The variable measured is discrete the distribution will be, fx - (8x1) + ( 9xy) +(1584) The mean g ř Ef It utst 8 tst utsty 424 11.777 36 So the mean is 11-777. Mode is the a ll. since it has mode of value with highest frequency. So the the distribution is frequency of 8. The median will be ize of item q (3+1) = size of (4.5)th item. th item th 11 size ME N+1 of of 2 - y the item t5th item 2 11 + 12 2 11.5

So the median is 11.5. 6) The weight of 40 The mean of Weight so -59 10 60-69 patients are given. the distribution will be calculated as Midpoint f fm 2 109 49.5-59.5 54.5 645 64.5 =59.5 - 69.5 13 74.5 69.5-79.5 9 68.5 79.5 - 89.5. 11 9 29.5 89.5 - 99.5 gy.5 283.5 = 9 9.5-109.5 104.5 1 104.5 70-79 84.5 80-89 11 3 go-gg 100-109 40 3040 76 The mean will be ñ £ fm 3040 Ef Yo 76. So the is mean as, 2 The variance will be given v(x) &fm² (8) Ef Elm? = (2x154.5) *)+(10 *[64.5)*)t- - + (1x (ov-st)

{fm² = 235950 235950 5898.75 {fm² &f Yo 2 So v(x) 5898.75 - ( 76) = /22.75 So the variance is 122.75. The standard deviation will be sp(x) 122.75 11.0792 11.0792 So the standard deviation is