Question

Choose the correct option for below statements.

Statement I: The mean always lies between the smallest and the largest values in a data set.

Statement II: The mean should be one of the given values of a data set.

• A. Only Statement I is correct.
• B. Both the statements are correct.

Answer 1

The correct option is A Only Statement I is correct.

Let's figure out the mean of an example data set before drawing any conclusions regarding the accuracy of the above statements:

Data 1	Data 2	Data 3
$1$	$2$	$4$

Mean/Average

$=\frac{\text{Sum of all data points}}{\text{Total number of data points}}$

$=\frac{1+2+4}{3}$
$=\frac{7}{3}$
$=\mathrm{2.3333...}$
$=2.\overline{3}$

Hence, the mean of the given data set $\{1,2,4\}$ is $2.\overline{3}$.

Here, we observe that

$\bullet$ The mean, $2.\overline{3}$, lies between the smallest $\left(1\right)$ and the largest $\left(4\right)$ values of the data set, i.e., $1<2.\overline{3}<4$.

$\bullet$ The mean, $2.\overline{3}$, is not one of the given values of the data set $\{1,2,4\}$.

So, in-general, we can conclude

$\bullet$ The mean always lies between the smallest and the largest values in a data set.

$\bullet$ The mean need not be one of the given values of a data set.

$\therefore$ Statement I is correct, but statement II is wrong.