Question

The annual rainfall record of a city of 100 days is given in the following table.calculate the median rainfall.
Rainfall no:of days
0-10 8
10-20 8
20-30 14
30-40 22
40-50 30
50-60 8
60-70 10

Answer 1

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Answer 2

Answer:

Median rainfall = 39.1

Step-by-step explanation:

Rainfall        no. of days         cumulative frequency

                       $f_i$

0-10                 8                               8

10-20               8                              16

20-30             14                              30

30-40             22                             52     —----> median class

40-50             30                             82

50-60               8                             90

60-70               10                            100

                    -------------

                      ∑$f_i$ = 100

Total frequency = N = ∑$f_i$ = 100

N/2 = 50

The median class is that class in which the cumulative frequency is just greater than $\frac{N}{2}$= 50

Hence median class is 30-40.

Median  = $L+{h (\frac{\frac{N}{2} -cf)}{f} )}$ -------------------(1)

L = Lower limit of the median class

h= width of the median class

N =  Total frequency

cf = cumulative frequency of the class preceding the median class

f = the frequency of the median class

here,

L = 30

h = 10

N = 100

cf = 30

f = 22

Substituting these values equation(1),

Median $= 30+ {10(\frac{50-30}{22} )$

$= 30+ {10(\frac{20}{22} )$

= 30+10X0.91

= 30+9.1

= 39.1

Hence, median rainfall = 39.1