Question

1. (15 Marks) The following are body mass index (BMI) scores measured in 11 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared 25, 27, 31, 28, 28, 41, 24, 32, 46, 35 and 40 Find the following a) Mean (I point) b) Meclion (1 point) c) Range (1 point) d) Lower Quartile (Q) (1 point) c) Upper Quartile (0) (1 point) ) Interquartile Range (IQR) (1 point) 8) Lower Fence (1 point) 1) Upper Fence (1 point) i) Construct a box-plot. Are there potential outliers in the data? Justify your answer (2 points)

Answer 1

Solution:
a)Mean

ˉx=∑x/n

=25+27+31+28+28+41+24+32+46+35+4011

=357/11

=32.4545


b)Median :
Observations in the ascending order are :
24,25,27,28,28,31,32,35,40,41,46

Here, n=11 is odd.

M= value of (n+12)th observation

= value of (11+12)th observation

= value of 6th observation

=31

c)Range

Range=(max value - min value)=(46-24)=22

d) Lower Quartile(Q1):-
Arranging Observations in the ascending order, We get :
24,25,27,28,28,31,32,35,40,41,46

Here, n=11

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

=(12/4)th value of the observation

=3rd value of the observation

=27