Question

If the mode of the following data $10,11,12,10,15,14,15,13,12,x,9,7$ is $15$, then the value of $x$ is:

• A. $10$
• B. $15$
• C. $12$
• D. $\frac{21}{2}$

Answer 1

The correct option is B $15$

The mode is the value which occurs the most often in a given set of data.
In the data set provided here, the mode is 15, hence 15 should occur the most number of times.
$10,11,12,10,15,14,15,13,12,x,9,7$
Excluding $x$ and arranging these numbers in ascending order,
$7,9,10,10,11,12,12,13,14,15,15$
Here 10, 12 and 15 are occurring twice.

Since 15 is the mode, it should occur more than twice.

Therefore, the value of $x$ should be 15 if the value of mode is 15.