Question

Find the values of the 30th & 90th percentiles from this data set :

7,12, 3, 14, 17, 20, 5, 3, 17, 4, 13, 2, 15, 9, 15, 18, 16, 9, 1, 9

Please explain - thanks in advance! :)

Answer 1

• 30th percentile = 5
• 90th percentile = 18

Explanation:

Arrange the values in increasing order :

⇒ 1, 2, 3, 3, 4, 5, 7, 9, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20

Finding the 30th percentile :

• Multiply 20 x 30%
• 6th term
• The 6th term is 5

Finding the 90th percentile :

• Multiply 20 x 90%
• 18th term
• The 18th term is 17

Answer 2

Hi!

The first thing I would do here is order the set of numbers, from smallest to largest. The order would be:

1, 2, 3, 3, 4, 5, 7, 9, 9, 9, 12, 13, 14, 15, 15, 16, 17, 17, 18, 20

The percentiles would be in the set, the number at the position of 30% and 90% out of the values in the entire set.

So essentially, since there are 20 values, you multiply 20 with 30% and 90% with 20 values, and you'll get the number of the value in the set which is at that percentile.

30% * 20 = 6

90% * 20 = 18

Now, just find the 6th and the 18th value.

The 6th is 5, and the 18th 17.

So your answer is, 30th percentile ~ 5, 90th percentile ~ 17

Hope this helps!