Class 10

Math

All topics

Statistics

In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.

Age (in year) | $0−15$ | $15−30$ | $30−45$ | $45−60$ | $60−75$ |

Number of patients | $5$ | $20$ | $40$ | $50$ | $25$ |

Class-Interval Frequency $Cf$

$0−15$ $5$ $5$

$15−30$ $20$ $25$

$30−45$ $40$ $65$

$45−60$ $50$ $115$

$60−75$ $25$ $140$

Where $cf=$ cumulative frequency

Median $=1+⎩⎨⎧ h×f(2N −cf) ⎭⎬⎫ $

Here:

$N=140$

$N/2=70$

$cf>70$ is $140$

Median class $=45−60$

So, $I=45,h=15,f=50$ and

$cf=cf$ of preceding class i.e. $65$

Substitute all the value in the above formula, we get

Median $=45+{15×(70−65)/50}$

$=45+1.5$

$=45.5$

Therefore , median age of diabetic patients is $46.5$ years.