Question

Find the 75th percentile.

2, 3, 5, 7, 10, 19, 22, 34

Answer 1

Answer:-

The p th 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 2,3,5,7,10,19,22,34.

Since, there are 8 values, then n=8.

Now, calculate the index

i=(p/100)⋅n

=(75/100)⋅8

=6

Since the index i is an integer, the 75th percentile is the average of the values at the positions i and i+1.

The value at the position i=6 is 19 and at the position i+1=7 is 22.

Their average is the percentile: (19+22)/2=41/2.

Answer: the 75th percentile is 41/2=20.5