Question

The arithmetic mean of the following data is 14, find the value of k.
xi:
5
10
15
20
25
fi:
7
k
8
4
5

Answer 1

Answer :

The value of k is 6.

Step-by-step explanation :

Arithmetic Mean -

Mean of a set of observations is obtained by dividing the sum of all observations by the total number of observations .

Mean = Sum of all observations / Total observations .

$Mean=\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

where $\Sigma$ means summation.

Frequency Distribution Table -

$\begin{tabular}{| c | c | c |}\cline{1-3}x_{i} & f_{i} & f_{i}x_{i} \\ \cline{1-3}5 & 7 & 35 \\ \cline{1-3}10 & k & 10k \\ \cline{1-3}15 & 8 & 120 \\ \cline{1-3}20 & 4 & 80 \\ \cline{1-3}25 & 5 & 125 \\ \cline{1-3} & \Sigma f_{i}=24+k & \Sigma f_{i}x_{i}=360+10k \\ \cline{1-3}\end{tabular}$

Since, mean -

$\implies\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

$\implies Mean=14$

$\implies 14=\frac{(360+k)}{(24+k)}$

$\implies 14\times (24+k)=(360+10k)$

$\implies 336+14k=360+10k$

$\implies 4k=24$

$\implies k=6$

Answer 2

We know that ,

Mean = Σfixi/Σfi = 14 [ given ]

=> ( 360 + 10k )/( 24 + k ) = 14

=> 360 + 10k = 14( 24 + k )

=> 360 + 10k = 336 + 14k

=> 360 - 336 = 14k - 10k

=> 24 = 4k

=> 4k = 24

=> k = 24/4

=> k = 6

Therefore ,

k = 6

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