Question

find the mean mode and median of the following data the class intervals are 0-20 20-40 40-60 60-80 80-100 100-120 120-140 and their frequencies are 12 13 6 7 8 14 and 13 respectively​

Answer 1

Answer:

N = 50 = N/2 = 25

median class =60 - 80

here, l = 60,f = 12,F = 24,h = 20

$median \: = \: l + \frac{ \frac{n}{2} - capitalf}{smallf} \times h$

$= 60 + \frac{25 + - 24}{12} \times 20$

$= 60 + \frac{1}{12} \times 20 = \frac{185}{3} = 61.6$

modal class = 60 - 80

l = 30,f = 12,f1 = 10,f2 = 6,h = 20

$mode = l + \frac{f - f1}{2f - f1 - f2} \times h$

$= 60 + \frac{12 - 10}{2 \times 12 - 10 - 6} \times 10$

$= 60 + \frac{2}{8} \times 20 = 65$

mode = 3median - 2mean

65=3 x (61.6) - 2mean

2mean = 184.8 - 65 = 58.68

$mean = \frac{119.8}{2} = 59.9$

hence,mean = 59.9 ,mode = 65 ,median = 61.6

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sorry vi forgot to add the table.

Answer 2

therefore,

Mode=65

Mean=62.4

Median=61.66

Step by step explanation in the above image...

Here,

Mode=l+[f1-f2/2f1-fo-f2]×h

l=lower limiit of the model class

h=Size of the class intervals

f1=frequency of modal class

fo= frequency of class preciding in the modal class

f2= frequency of succeeding in the modal class

Median:l+[n/2-cf/f]×h

l= lower limit of the median class

h=number of observations

cf=cumulative frequency of class interval pre eding in median class

f=frequency of median class

h=class height

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