Question

The age of a patient at the time of diagnosis of colon cancer was tracked—50 males and 50 females. The ages are:

M: 91 87 87 85 83 81 80 79 78 77 75 75 74 73 72 72 71 71
70 69 69 68 66 66 65 63 63 63 62 62 62 61 61 61 60 60
59 59 57 56 55 55 53 53 51 48 45 39 38 29
F: 94 93 92 90 89 88 87 86 86 85 85 83 81 79 79 78 77 77
76 76 76 76 75 74 74 73 72 72 71 70 68 68 67 66 66 65
65 6564 64 64 63 60 59 58 55 54 53 51 48

a. Calculate the range for males........... , females ............ , and combined ...............

b. Calculate the average age for men (compute to the second decimal) ............ .

c. Calculate the value for:
85th percentile for the combined ages...........
Percentile for an age of 60 for females............ th
Percentile for an age of 75 for males. .......... th

2-calculate the average age for men (compute to the second decimal)................

3- Calculate the value for:

(1) 85th percentile for the combined ages..........
(2) Percentile for an age of 60 for females........... th
(3) Percentile for an age of 75 for males............. th

Answer 1

Part a)

Calculate Range of Male

Range = Maximum Value - Minimum Value = 91 - 29 = 62

Calculate Range of Female

Range = Maximum Value - Minimum Value = 94 - 48 = 46

Combine Range

Combining the data of Male and Female

Range = Maximum Value - Minimum Value = 94 - 29 = 65

Part b) Average age of men  

Mean = = 3259 / 50 = 65.18

85^th percentile for the combined ages

Solution :- Combine the data of male and female and arrange the data in ascending order

85^th Percentile can be calculate by 85% * ( sample size + 1 )

85% * (100+1) = 85.85    86

So we have 85 on 86^th Place

85^th Percentile = 85

Percentile for an age of 60 for females

Solution :- Percentile rank of X = ( Number of values below X) / n * 100

Arrange the data of female in ascending order

Percentile rank of 60 =  ( Number of values below 60) / 50 * 100

Percentile rank of 60 = 7 / 50 * 100 = 14^th percentile

Percentile for an age of 75 for males

Solution :-

Percentile rank of X = ( Number of values below X) / n * 100

Arrange the data of male in ascending order

Percentile rank of 75 =  ( Number of values below 75) / 50 * 100

Percentile rank of 75 = 38 / 50 * 100 = 76^th percentile