An administrative assistant collected data on average minutes spent commuting for the 16 employees in the office. The data is ranked below:
5, 8, 10, 10, 12, 15, 15, 15, 15, 15, 15, 20, 20, 20, 25, 60
What is the value of the number that splits the lowest 25% of the sample from the highest 75% of the sample (Q1)?
A) 60
B) 12
C) 5
D) 8

Question

Quizplus · Accepted Answer

Q1, also known as the 25th percentile, is the value that separates the lowest 25% of the data from the highest 75%. To find Q1, we need to determine the position of the median (which is also the 50th percentile) within the first quartile of the data. Since there are 16 data points, the median is the average of the 8th and 9th values (15+15)/2 = 15. The 25th percentile would then be the median of the four values to the left of the median, which are 5, 8, 10, and 10. The median of these four is (8+10)/2 = 9, which is the value that splits the lowest 25% of the sample from the highest 75%. Therefore, the answer is (B) 12.

An Administrative Assistant Collected Data on Average Minutes Spent Commuting