Question

For the data $1,5,7,x+1,9,x-2,3$, if mean is $4$, find the value of $x$. Also, find the mode of the data.

Answer 1

Step 1: Find the value of $x$

Given: The observations are $1,5,7,x+1,9,x-2,3$. The mean of the given observations is $4$.

Mean = $\frac{Sumofallobservations}{totalnumberofobservations}$

$\therefore 4=\frac{1+5+7+x+1+9+x-2+3}{7}$

$\Rightarrow 28=24+2x$

$\Rightarrow 2x=4$

$\Rightarrow x=2$

Step 2: Find the mode

Now, the observations are $1,5,7,3,9,0,3$

Mode is that value that occurs most frequently.

Therefore the mode is $3$

Hence, the value of $x$ is $2$ and the mode of the given observations is $3$.