Question

If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using this value of x, find the mode of the data.

Answer 1

We know that,

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observa}\mathrm{tions}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

The given data is 3, 21, 25, 17, (x + 3), 19, (x – 4).

Mean of the given data = $\frac{3+21+25+17+\left(x+3\right)+19+\left(x-4\right)}{7}$
$$\begin{gathered} \Rightarrow 18\left(7\right)=84+2x \\ \Rightarrow 126-84=2x \\ \Rightarrow 2x=42 \\ \Rightarrow x=21 \end{gathered}$$

Hence, the value of x is 21.

Now, the given data is 3, 21, 25, 17, 24, 19, 17
Arranging this data in ascending order:
3, 17, 17, 19, 21, 24, 25

Here, 17 occurs maximum number of times.
∴ Mode = 17

Hence, the mode of the data is 17.