Consider the following frequency distribution : Class: 10-20, 20-30,30-40,40-50,50-60 Frequency: α,110,54,30,β

Question

Consider the following frequency distribution :

Class:	10-20	20-30	30-40	40-50	50-60
Frequency	α	110	54	30	\(\beta\)

If the sum of all frequencies is 584 and median is 45, then |α - \(\beta\)| is equal to _______.

Answer 1

Correct answer 164

\(\because\) sum of frequencies = 584

\(\Rightarrow\) α + β = 390

Now, median is at \(\frac{584}{2} = 292^{th}\)

\(\because\) median = 45 (lies in class 40 -50)

\(\Rightarrow\) α + 110 + 54 + 15 = 292

\(\Rightarrow\) α = 113, β = 277

\(\Rightarrow\) |α - β| = 164