Question

1. A local hospital collects monthly data on the number of infections after surgeries. These data are shown below:

209	225	201	236	220	244	247	245	250	227
234	227	213	212	193	182	242	230	188	252
201	226	222	212	219	223	191	222	231	239
217	241	220	278	255	225	208	225	227	203

Determine the lower and upper quartiles.

Answer 1

Arranging Observations in the ascending order, We get :
182,188,191,193,201,201,203,208,209,212,212,213,217,219,220,220,222,222,223,225,225,225,226,227,227,227,230,231,234,236,239,241,242,244,245,247,250,252,255,278

Here, n=40

Q1=(n+1/4)th value of the observation

=(41/4)th value of the observation

=(10.25)th value of the observation

=10th observation +0.25[11th-10th]

=212+0.25[212-212]

=212+0.25(0)

=212+0

=212

Q3=(3(n+1)4)th value of the observation

=(3⋅41/4)th value of the observation

=(30.75)th value of the observation

=30th observation +0.75[31st-30th]

=236+0.75[239-236]

=236+0.75(3)

=236+2.25

=238.25