Question

In the following dataset, mode with outlier is , and mode without outlier is .

$1$

$0$

$1$

$5$

$6$

$3$

$4$

$15$

$15$

• A. $1$
• B. $15$
• C. $1\text{or}15$
• D. $1\text{and}15$

Answer 1

Answer: (A), (D)

$1\text{and}15$

In the given data set, except the number $15$, all the remaining data points lie between $0$ and $6$. So, the outliers of the given data set are $15$ and $15$.

$\bullet$ On arranging the data set with outliers in an increasing order, we get

$0$

$\underset{–}{1}$

$\underset{–}{1}$

$3$

$4$

$5$

$6$

$\underset{–}{15}$

$\underset{–}{15}$

Here, both the numbers $1$ and $15$ repeat twice, which is the maximum number of occurrence in the data set.

$\therefore$ The modes of the data set with outliers are $1$ and $15$.

$\bullet$ The given ordered data set without outliers is

$0$

$\underset{–}{1}$

$\underset{–}{1}$

$3$

$4$

$5$

$6$

Here, only the number $1$ repeats twice, which is the maximum number of occurrence in the data set.

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