JEE MAIN - Mathematics (2021 - 25th July Morning Shift - No. 16)
Consider the following frequency distribution :
If the sum of all frequencies is 584 and median is 45, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to _______________.
| Class : | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
|---|---|---|---|---|---|
| Frequency : | $$\alpha $$ | 110 | 54 | 30 | $$\beta $$ |
If the sum of all frequencies is 584 and median is 45, then | $$\alpha$$ $$-$$ $$\beta$$ | is equal to _______________.
Answer
164
Explanation
$$\because$$ Sum of frequencies = 584
$$\Rightarrow$$ $$\alpha$$ + $$\beta$$ = 390
Now, median is at $${{584} \over 2}$$ = 292th
$$\because$$ Median = 45 (lies in class 40 - 50)
$$\Rightarrow$$ $$\alpha$$ + 110 + 54 + 15 = 292
$$\Rightarrow$$ $$\alpha$$ = 113, $$\beta$$ = 277
$$\Rightarrow$$ | $$\alpha$$ $$-$$ $$\beta$$ | = 164
$$\Rightarrow$$ $$\alpha$$ + $$\beta$$ = 390
Now, median is at $${{584} \over 2}$$ = 292th
$$\because$$ Median = 45 (lies in class 40 - 50)
$$\Rightarrow$$ $$\alpha$$ + 110 + 54 + 15 = 292
$$\Rightarrow$$ $$\alpha$$ = 113, $$\beta$$ = 277
$$\Rightarrow$$ | $$\alpha$$ $$-$$ $$\beta$$ | = 164
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