Question

John's Science book has $10$ chapters. The number of pages in each of the $10$ chapters are $25,11,9,18,21,24,16,13,30,12$. If two new chapters with $60$ and $65$ pages are added in the book, what would be the effect on median of the dataset?

• A. Median will increase.
• B. Median will decrease.
• C. Median will be same.
• D. Cannot be determined

Answer 1

The correct option is A Median will increase.

The given data set for the number of pages in $10$ chapters is

$25$

$11$

$9$

$18$

$21$

$24$

$16$

$13$

$30$

$12$

$\bullet$ After arranging the above data set in ascending order, we get

$9$

$11$

$12$

$13$

$\underset{–}{16}$

$\underset{–}{18}$

$21$

$24$

$25$

$30$

The median of the above ordered data set $=$ mean of $5^{\text{th}}\&6^{\text{th}}$ data points$=\frac{16+18}{2}=17$

$\bullet$ The data set for the number of pages in $12$ chapters, i.e., including two chapters with page numbers $60$ and $65$ in ascending order is

$9$

$11$

$12$

$13$

$16$

$\underset{–}{18}$

$\underset{–}{21}$

$24$

$25$

$30$

$60$

$65$

$\underset{–}{\text{Note:}}$ In the above data set, except $60$ and $65$, all the remaining data points lie between $9$ and $30$. So, the ouliers of the above data set are $60$ and $65$.

The median of the above ordered data set $=$ mean of $6^{\text{th}}\&7^{\text{th}}$ data points $=\frac{18+21}{2}=19.5$

So, we get
median without outliers= $17$
median with outliers= $19.5$

Here, we can see on including the outliers (two chapters with $60\&65$ pages), the median of the dataset is increased, i.e., option (a.) is the correct one.

$\underset{–}{\text{Note:}}$ Although we have added two large outliers ($60\&65$) as compared to the remaining data points, the median value is NOT increased significantly. So, we can also conclude that an outlier does not shift the median much.