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The mean of the frequency table given below is 50. Then find out the values of a and b.

classfrequency
0-20
20-40
40-60
60-80
80-100
17
a
32
b
19
total120

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Best answer
Mid valueFrequencyClass average x
frequency
10
30
50
70
90
17
a
32
b
19
170
30a
1600
70b
1710
total1203480+30a+70b

 mean = 50

\(\therefore\) \(\cfrac{3480+30a+70b}{120}\) = 50

30a + 70b = 6000 – 3480

30a + 70b = 2520 (1)

17 + 32 + 19 + a + b = 120 

68 + a + b = 120,

a + b = 52 (2) 

(2) x 30 => 30a + 30b = 1560

30a + 70b = 2520,

30a + 30b = 1560,

40b = 960,

b = 960/40 = 24,

a + 24 = 52

a = 52 – 24 = 28,

\(\therefore\) a = 28, b = 24

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