Question

the mean of the following distribution is 50;
find the value of 'a' and hence the frequentcies of 30 & 70

Answer 1

Hi ,

We know that ,
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Mean = sigma(fx) / sum of the frequecies ----( 1 )

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Sum of the frequencies

= 17 + ( 5a + 3 ) + 32 + 7a - 11 +19 = 60 + 12a -------( 2 )

Sum of ( fx )

= 17 × 10 + 30 ( 5a + 3 ) + 50 × 32 + 70 ( 7a - 11 ) + ( 90 + 19 )

= 170 + 150a + 90 + 1600 + 490a - 770 + 1710

= 2800 + 640a -----( 3 )

According to the given problem ,

Mean = 50

( 3 ) / ( 2 ) = 50 [ from ( 1 ) ]

[ 2800 + 640a ] / ( 60 + 12a ) = 50

2800 + 640a = 50 ( 60 + 12a )

2800 + 640 a = 3000 + 600a

640 a - 600a = 3000 - 2800

40a = 200

a = 200 / 40

a = 5

Therefore,

Frequeny of 30 = 5a + 3 = 5 × 5 + 3 = 25 + 3 = 28

Frequecy of 70 = 7a - 11 = 7 × 5 - 11 = 35 -11 = 24

I hope this helps you.

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Answer 2

Hi there!

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What is Mean?

The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = $\frac{Sum \: of \: observations }{Number \: of \: observations }$

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For your solution to the given question refer to the attachment.

Thanks for the question!

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