Question

The arithmetic mean of the following data is 25, find the value of k.
xi:
5
15
25
35
45
fi:
3
k
3
6
2

Answer 1

ARITHMETIC MEAN OR MEAN OR AVERAGE :  

The arithmetic mean of a set of observations is obtained by dividing the sum of the values of all observations by the total number of observations .

Mean = Sum of all the observations / Total number of observations .

MEAN = Σfixi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfixi = 390 + 15k  ,Σfi = 14 + k

MEAN = Σfixi / Σfi  

Given : Mean = 25

25 = (390 + 15k) / (14 + k )  

25 × (14 + k ) = (390 + 15k)

350 + 25k = (390 + 15k)

25k - 15k = 390 - 350

10k = 40

k = 40/10 = 4

k = 4

Hence, the value of k is 4 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

We know that ,

Mean = Σfixi /Σfi = 25 [ Given]

=> ( 390 + 15k )/( 14 + k ) = 25

=> 390 + 15k = 25( 14 + k )

=> 390 + 15k = 350 + 25k

=> 390 - 350 = 25k - 15k

=> 40 = 10k

=> ( 40/10 ) = k

=> 4 = k

k = 4

Therefore ,

k = 4

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