Question

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Answer 1

X= 20

Explanation:

Given : mean of the following distribution is 50.

Class Interval 0-20 20-40 40-60 60-80 80-100

Frequency 34 3x-4 64 48 2(x-1)

To Find : the value of x

Solution:

Class Interval Class mark xi f xif

0-20 10 34 10(34)

20-40 30 3x-4 10(3)(3x - 4)

40-60 50 64 10(5)(64)

60-80 70 48 10(7)(48)

80-100 90 2(x -1 ) 10(9)(2(x - 1)

140 + 5x 10(660 + 27x)

(140 + 5x)50 = 10 (660 + 27x)

=> (140 + 5x)5 = (660 + 27x)

=>700 + 25x = 660 + 27x

=> 2x = 40

=> x = 20

Answer 2

The value of x is 20

x = 20

Explanation:

The formula for mean is,

Mean = (Sum of( interval midpoint times frequency))/(sum of frequencies)

Sum of frequencies = 34 + 3x - 4 + 64 + 48 + 2x - 2

Sum of frequencies = 140 + 5x

now,

the midpoints are,

Midpoint = 1/2(upper term + lower term)

for 0-20, 20-40, 40-60, 60-80, 80-100

Midpoint 10 , 30 , 50 , 70 , 90

Now, finding the sum of frequency * midpoint,

sum = (34)(10) + (3x - 4)(30) + (64)(50) + (48)(70) + (2x - 2)(90)

sum = 340 + 90x - 120 + 3200 + 3360 + 180x - 180

sum = 6600 + 270x

So, we get the mean,

Mean = (6600 + 270x)/(140 + 5x)

we are given that mean = 50,

so,

50 = (6600 + 270x)/(140 + 5x)

50(140 + 5x) = 6600 + 270x

7000 + 250x = 6600 + 270x

7000 - 6600 = 270x - 250x

400 = 20x

400/20 = x

x = 20