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One healthcare center working for the welfare of the patients suffering from 'Dengue', recorded the following information :
Age of Patients
quad Number of Patients
$0-15$
quad $8$
$15-30$
quad $5$
$30-45$
quad $x$
$45-60$
quad $16$
$60-75$
quad $12$
$75-90$
quad $9$
If the modal age of the patients is $54$, then find the value of $x$.
Age of Patients
quad Number of Patients
$0-15$
quad $8$
$15-30$
quad $5$
$30-45$
quad $x$
$45-60$
quad $16$
$60-75$
quad $12$
$75-90$
quad $9$
If the modal age of the patients is $54$, then find the value of $x$.
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Modal class is $45 - 60$
Mode = $54$
$\therefore 45 + \left(\frac{16-x}{2\times 16-x-12}\right) \times 15 = 54$
$\Rightarrow x = 10$
Mode = $54$
$\therefore 45 + \left(\frac{16-x}{2\times 16-x-12}\right) \times 15 = 54$
$\Rightarrow x = 10$