Question

Qn4. Persons suffering from a blood disease are found to have an abnormality in one particular chromosome. However, not all samples of this chromosome are abnormal, and in order to estimate the proportion of affected ones, 5 samples of this chromosome are examined from each of 120 patients, the number of affected one, r, being recorded for each patient. The results are tabulated below;
r 0 1 2 3 4 5
frequency (f) 6 31 42 29 10 2

REQUIRED:
i.) Estimate the proportion 'p' of affected chromosomes and hence
ii.) Compute their variance. (4 Marks)

Answer 1

p(5)=x/n=2/120=0.0167

p(4)=10/120=0.083

p(3)=29/120=0.2416

p(2)=42/120=0.35

p(1)=31/120=0.2583

p(0)=6/120=0.05

$\bar x = (\sum fx)/n$ =252/120=2.1

$variance=S^2 = (\sum f*x^2 - (\sum f*x)^2/n)/(n-1)=(670 - (252)^2/120)/119=1.1832$