Question

Given below is the data set for the number of states visited by the students.


Mode with outlier $-$ Mode without outlier $=$ .

• A. $1$
• B. $-1$
• C. $0$

Answer 1

The correct option is C $0$

In the given data set, except $19$, all the remaining data points lie between $0$ and $10$. So, the outlier of the data set is $19$.

$\bullet$ Given dataset with an outlier in increasing order:


Here, the data point $1$ occurs the maximum number of times, i.e., $4$.

$\therefore$ The mode of the data set with outlier is $1$.

$\bullet$ Given ordered data set without outlier:


Here also, the data point $1$ occurs the maximum number of times, i.e., $4$ times.

$\therefore$ The mode of the data set without outlier is also $1$.

So, we get
mode with outlier $=1$
mode without outlier $=1$

Finally,
Mode with outlier $-$ Mode without outlier
$=1-1$
$=0$

$\underset{–}{\text{Note:}}$ For the given data set, mostly an outlier does not change the mode.