Question

39. Find the median for the given frequency distribution:
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Answer 1

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Answer 2

$MEDIAN = l+\frac{(\frac{n}{2}-c.f.) }{f}* h$

where,

• l is the lower limit of median class

• n is the total frequency

• c.f. is the cumulative frequency of class preceding the median class

• f is the frequency of median class

• h is the class size

let us firstly draw a cumulative frequency distribution table

class → frequency→ cumulative frequency

40-45→2→2

45-50→3→5

50-55→8→13

55-60→6→19

60-65→6→25

65-70→3→28

70-75→2→30

now median class will be 55-60

so,

l=55

n=30

c.f.=13

f=6

h=5

putting values in the formula of median

$median = 55+\frac{(\frac{30}{2}-13) }{6} *5\\\\median = 55+\frac{2}{6} *5\\\\median=\frac{55}{1} +\frac{10}{6} \\\\median= \frac{330+10}{6} \\\\median = \frac{340}{6} \\\\median = 56.67$

MEDIAN OF THE DATA GIVEN WILL BE 56.67 .