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

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 = (360 + 10k)  ,Σfi = (24 + k )

MEAN = Σfixi / Σfi  

Given : Mean = 14  

14 = (360 + 10k) / (24 + k )  

14 × (24 + k ) = (360 + 10k)  

336 + 14k = (360 + 10k)  

14k - 10k = 360 - 336  

4k = 24

k = 24/4 = 6  

k = 6  

Hence, the value of k is 6 .  

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

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 -

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

Since, mean -

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

$\implies Mean=14$

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

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

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

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

$\implies 4k=24$

$\implies k=6$