Question

50 persons were examined through X-ray and observations were noted as under:

Diameter of heart (in mm) : 120,121,122,123,124

Number of patients: 5,8,12,9,6,10

Find:

(i) The mean diameter of heart,

(ii) The median diameter of heart.

Answer 1

Diameter of heart (in mm)(xi)	Number of patients (Frequecy) (fi)	fixi	cumulative frequency (C.F.)
120	5	600	5
121	8	968	13
122	12	1464	25
123	9	1107	34
124	6	744	40
125	10	1250	50
	n = \(\sum\)fi = 50	\(\sum\)fixi = 6133

\(\therefore\) Mean = \(\frac{\sum f_ix_i}{\sum f_i}\) = \(\frac{6133}{50} \) = 122.66

\(\frac{n}2=\frac{50}2=25\)

\(\therefore\) l = 122, c = 13, f = 12, h = 1

Medium = l + \(\cfrac{\frac{n}2-c}{f}\times h\) 

 = 122 + \(\frac{25-13}{12}\times 1\) 

 = 122 + \(\frac{12}{12}\times1\) 

 = 122 + 1 = 123

Hence, medium diameter of heart is 123 mm