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Finding Median for Grouped Data When Class Intervals Are Given

Find the medi...

Question

Find the median if total students are $40$
Weight $45$ $46$ $47$ $48$ $49$ $50$ $51$ $52$ $53$
Median $6$ $2$ $3$ $4$ $7$ $4$ $7$ $4$ $3$

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Solution

Median $= \frac{1}{2} ({\frac{n}{2}}^{t h} o b s e r + {(\frac{n}{2} + 1)}^{t h} o b s e r)$
$\begin{matrix} = \frac{1}{2} (20^{t h} + 21^{t h}) = \frac{1}{2} (49 + 49) = 49 \end{matrix}$

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20

Weight(in kg)	$47$	$50$	$53$	$56$	$60$
Number of students	$4$	$3$	$7$	$2$	$4$

83, 66, 86, 30, 82

45, 49, 46, 44, 38, 37, 55, 51

70, 71, 70, 68, 67, 69, 70

51, 55, 46, 47, 53, 55, 51, 46

Weight (in kg)	45	46	48	50	52	54	55
Number of students	8	5	6	9	7	4	2

k g

13

44

42

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52

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49

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Weight	$45$	$46$	$47$	$48$	$49$	$50$	$51$	$52$	$53$
Median	$6$	$2$	$3$	$4$	$7$	$4$	$7$	$4$	$3$