A researcher has collected some data on the amount of time in seconds (to the nearest 0.1 second) that it took trained rats to run through a maze. The data is shown below arranged in a frequency distribution of grouped scores. The 75th percentile point is _________.
A) 6.42
B) 6.87
C) 6.82
D) 6.47

Question

A researcher has collected some data on the amount of time in seconds (to the nearest 0.1 second) that it took trained rats to run through a maze. The data is shown below arranged in a frequency distribution of grouped scores.  The 75th percentile point is _________.
A) 6.42 
B) 6.87 
C) 6.82 
D) 6.47

Quizplus · Accepted Answer

To find the 75th percentile point, we need to calculate the cumulative frequency (CF) of each score in the frequency distribution. Then, we find the score that corresponds to the 75th percentile using the formula:

75th percentile = L + [(N/4 - CF of the score before the 75th percentile)/f] × i

where L is the lower limit of the interval containing the 75th percentile, N is the total number of scores, CF is the cumulative frequency, f is the frequency of the interval containing the 75th percentile, and i is the interval size.

Using this formula, we can calculate the 75th percentile as:

L = 6.8
N = 30
CF of the score before the 75th percentile = 17
f = 6
i = 0.1

75th percentile = 6.8 + [(30/4 - 17)/6] × 0.1 = 6.82

Therefore, the 75th percentile point is 6.82 seconds.

A Researcher Has Collected Some Data on the Amount of Time