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

Diameter of heart (in mm)	Number of patients
120	5
121	8
122	12
123	9
124	6
125	10

Find :

(i) The mean diameter of heart,

(ii) The median diameter of heart.

(i) We know that,

$\Rightarrow \text{Mean} = \dfrac{\text{Σfx}}{\text{Σf}} \\[1em] \Rightarrow \text{Mean} = \dfrac{6133}{50} \\[1em] \Rightarrow \text{Mean} = 122.66 \text{ mm}.$

Hence, mean diameter of heart = 122.66 mm.

(ii) Here,

Number of observations (n) = 50, which is even.

By formula,

$\Rightarrow \text{Median} = \dfrac{\Big(\dfrac{\text{n}}{2}\Big) \text{th} \text{ term} + \Big(\dfrac{\text{n}}{2} + 1\Big)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\Big(\dfrac{50}{2}\Big) \text{th} \text{ term} + \Big(\dfrac{50}{2} + 1\Big)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{25 \text{th} \text{ term} + (25 + 1)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{25 \text{ th} \text{ term} + 26\text{ th} \text{ term}}{2}$

From table,

Diameter of heart corresponding to 25th term is 122

Diameter of heart corresponding to 26th term is 123

$\Rightarrow \text{Median} = \dfrac{25 \text{th} \text{ term} + 26\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{122 + 123}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{245}{2} \\[1em] \Rightarrow \text{Median} = 122.5 \text{ mm}.$

Hence, median diameter of heart = 122.5 mm.