Question

# The following frequency table summarizes 60 data values. What is the 80th percentile of the data?...

The following frequency table summarizes 60 data values. What is the 80th percentile of the data? The table is read from left to right.

 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 6 6 6 7 7 8 8 9 9 9 9 10 11 11 11 11 11 12 12 12 12 13 13 13 14 14 14 14 15 15 15 16 17 17 17 17 17 18 19 19 20 20 20 20 20

The pth percentile is a value such that at least p percent of the observations is less than or equal to this value and at least (100−p) percent of the observations is greater than or equal to this value.

The first step is to sort the values.

The sorted values are 1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,6,6,6,7,7,8,8,9,9,9,9,10,11,11,11,11,11,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16,17,17,17,17,17,18,19,19,20,20,20,20,20

Since there are 60 values, then n=60.

Now, calculate the index

Since the index i is an integer, the 80th percentile is the average of the values at the positions i and i+1.

The value at the position i=48 is 17 and at the position i+1=49 is 17.

Their average is the percentile:

Answer: the 80th percentile is 17.