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Find the mean and mode of the following frequency distribution :
Class Interval: $400-450$ $450-500$ $500-550$ $550-600$ $600-650$ $650-700$
Frequency: $15$ $18$ $20$ $23$ $22$ $12$
Class Interval: $400-450$ $450-500$ $500-550$ $550-600$ $600-650$ $650-700$
Frequency: $15$ $18$ $20$ $23$ $22$ $12$
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Sol. Correct table (I Mark)
Mean = $525 + \frac{55}{110} \times 50$ (II Mark)
$= 550$ (III Mark)
Modal class is $550 - 600$ (IV Mark)
Mode = $550 + \frac{23 - 20}{46 - 20 - 22} \times 50$ (V Mark)
$= \frac{1175}{2} = 587.5$ (VI Mark)
Mean = $525 + \frac{55}{110} \times 50$ (II Mark)
$= 550$ (III Mark)
Modal class is $550 - 600$ (IV Mark)
Mode = $550 + \frac{23 - 20}{46 - 20 - 22} \times 50$ (V Mark)
$= \frac{1175}{2} = 587.5$ (VI Mark)