Question

The outliers are removed from the following data set.

$10$

$50$

$55$

$55$

$60$

$62$

$105$

Which of the following options is true for the mean of the data set after removing the outliers?

• A. Mean will increase
• B. Mean will decrease
• C. Mean will be same

Answer 1

The correct option is B Mean will decrease

In the given data set, except $10$ and $105$, all the remaining data points lie in between $50$ and $65$. So, the outliers of the given data set are $10$ and $105$, which are the smallest and the largest numbers of the data set, respectively.

$\underset{–}{10}$

$50$

$55$

$55$

$60$

$62$

$\underset{–}{105}$

The mean of the data set with ouliers is
$\frac{10+50+55+55+60+62+105}{7}$
$=\frac{397}{7}=56.71$

The mean of the data set without ouliers is
$\frac{50+55+55+60+62}{5}$
$=\frac{282}{5}=56.40$

So, we get
$\bullet$ mean with outliers= $56.71$
$\bullet$ mean without outliers= $56.40$

Hence, we can see on excluding outliers, mean value of the dataset is decreased.

$\therefore$ We can conclude that an outlier skews the value of the mean.