The sample data below shows the number of hours spent by five students over the weekend to prepare for Monday's Business Statistics exam. (See the Excel Data File.) The 75^th percentile of the data is the closest to ________. A) 3 hours B) 4.5 hours C) 8.5 hours D) 10 hours

Question

Quizplus · Accepted Answer

To find the 75th percentile, we need to arrange the data in order: 
2, 3, 4, 8, 10

The formula for finding the percentile is: 
Percentile = (P/100) * (n+1)  
where P = percentile value, n = number of values

Substituting the values we get, 
Percentile = (75/100) * (5+1) 
= 4.5

Since 4.5 falls between 4 and 8, we need to interpolate: 
Lower value = 4 
Upper value = 8 
Difference = 8-4 = 4

Percentile value = Lower value + (percentile difference/interval) * (Upper value - Lower value) 
Percentile value = 4 + (0.5/1) * 4 
Percentile value = 8.

Therefore, the 75th percentile of the data is closest to 8.5 hours, which is option C.

The Sample Data Below Shows the Number of Hours Spent