Consider the following frequency distribution :
class $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$
Frequency $α$ $110$ $54$ $30$ $β$
If the sum of all frequencies is $584$ and median is $45$ , then $| α - β |$ is equal to .

Question

Consider the following frequency distribution :

class	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$α$	$110$	$54$	$30$	$β$

If the sum of all frequencies is $584$ and median is $45$ , then $| α - β |$ is equal to .

TestHub · Accepted Answer

∵ Sum of frequencies = 584 α + 110 + 54 + 30 + β = 584 ⇒ α + β = 390 . . . 1 Now, Median is at 584 2 = 292 th term ∵ Median = 45 (lies in class 40 - 50 ) ⇒ α + 110 + 54 + 15 = 292 ⇒ α = 113 . . . 2 On solving, equations 1 and 2 , we get ⇒ α = 113 & β = 390 - 113 = 277 ⇒ | α - β | = 164

Mathematics - Statistics Question with Solution | TestHub

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