Consider the following frequency distribution : If the sum of all frequency is 584 and median is 45

Question

Consider the following frequency distribution :  If the sum of all frequency is 584 and median is 45 , then $|\alpha-\beta|$ is equal to

Professor PC Thomas Classes · Answer

(164) : \ Given, sum of frequency $=584$\ $\Rightarrow \alpha+\beta=390$\ Median $=l+\left[\frac{\left(\frac{N}{2}ight)-	ext { c.f. }}{f}ight] 	imes n$\ $\because \quad \frac{N}{2}=\frac{584}{2}=292$\ $	herefore \quad M=40+\left[\frac{292-(\alpha+164)}{30}ight] 	imes 10$\ $\Rightarrow \quad 45=40+\left(\frac{128-\alpha}{3}ight)$\ $\Rightarrow \quad 15=128-\alpha \Rightarrow \alpha=113$ and $\beta=277$\ $	herefore \quad|\alpha-\beta|=|113-277|=164$\