Question

3. The Putnam is a yearly mathematics competition for college students. In 2016, the median score was a 1 out of 120) If you had a histogram of the 4164 participants from 2016, how would it be skewed? What additional information would you need about the data set to decide if outliers were present based on the outlier definition related to boxplots? If you want to see what the exam looks like, visit here, a site maintained by UCSD prof and crossword speed-solver Kiran Kedlaya.

Answer 1

If the median score is 1 out of 120 for 4164 participants

The histogram of the data will be right skewed

To decide the outliers with definitions related to box plot, the definition is

a data point is an outlier if it is more than 1.5 * IQR1 above the third quartile or below the first quartile.

Said differently, low outliers are below Q1−1.5*IQR

and high outliers are above Q3+1.5*IQR

To understand the outliers we need

- Q1 - Quartile 1 (25th percentile of the data)

- Q3 - Quartile 3 (75th percentile of the data)

IQR will be calculated as Q3 - Q1