Question

Find the median of the following data:
Marks frequency
less than 10 0
less than 30 10
less than 50 25
less than 70 43
less than 90 65
less than 110 87
less than 130 96
less than 150 100

Answer 1

Answer: The median of the given data is 76.36

Step-by-step explanation:

First we will find $\dfrac{n}{2} = \dfrac{100}{2} =50$

Therefore from attached table we have CF= 43 , f = 22  and L= 70

As we know  

$\text{Median} = L +\dfrac{\dfrac{n}{2}-CF }{f} \times h\\\\=70 + \dfrac{50-43}{22} \times 20\\\\=70+ \dfrac{7}{22} \times 20\\\\=70 +\dfrac{140}{22} =  70+ 6.36=76.36$

Hence, the median of the given data is 76.36

Answer 2

Median = 76.36

Step-by-step explanation:

Class interval Frequency  Cumulative frequency  

0−10                            0                      0  

10−30                           10                       10  

30−50                            15                25  

50−70                            18                43  

70−90                           22                65  

90−110                           22                 87  

110−130                            9                        96  

130−150                    4                       100

N = 100, N/2 = 50

The cumulative frequency just greater than N/2 = 50, then median class is 70−90 such that,

lower limit =70,

width of the median class(h)  =  90−70 =20,

f = 22, cf = 43

Median = L + $\frac{\frac{9}{2} - CF }{f}$ × h

= 70 + $\frac{50-43}{22}$ × 20

= 76.36

Learn more: calculate the median

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