Answer to Question #248395 in Statistics and Probability for Colour

Question

Mia took a survey of students in her class to find put how many hours they spend reading each week. Here are some summary statistics for the data that mia gathered. Mean: 8.5 hours, median: 7 hours, standard deviation: 5.3 hours, Q1: 5 hours, Q3: 11 hours.

Give an example of a number of hours larger than the median which would be an outlier. Explain your reasoning.

Answer 1

25 hours

This is an extreme value from the center of data collected

As per Turkey's method, an outliers greater than median lies beyond the upper boundary of Q₃ +1.5 IQR

Where:

Q₃ is the third quartile

IQR is the interquartile range

IQR=Q₃ - Q₁

Where Q₁ is the first quartile

Therefore upper boundary

= 11+1.5(11-5)

=11+1.5×6

=20 hours

25 hours is an outlier since it is beyond upper fence of 20 hours