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

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

 class frequency 0-2020-4040-6060-8080-100 17a32b19 total 120

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 Mid value Frequency Class average xfrequency 1030507090 17a32b19 17030a160070b1710 total 120 3480+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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