Question

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 21st, 26th, 60th, and 70th percentiles. If needed, round your answers to two decimal digits.

Answer 1

From the given information, the sample data values are 27, 25, 20, 15, 30, 34, 28, and 25.

The sample size is n = 8.

Arrange the data values in ascending order: 15, 20, 25, 25, 27, 28, 30, and 34.

Compute the index value associated with the 21st percentile.

i = (p/100 )*n
= (21/100)*8
= 1.68

The index value is not an integer. Round 1.6 to 2. The value is the 2nd value in the sorted data set.

Therefore, the 20th percentile value is 20.

i = (p/100 )*n
= (26/100)*8
= 2.08

The index value is not an integer. Round 2.08 to 2. The value is the 2nd value in the sorted data set.

Therefore, the 26th percentile value is 20.

i = (p/100 )*n
= (60/100)*8
= 4.8

The index value is not an integer. Round 4.8 to 5. The value is the 5th value in the sorted data set.

Therefore, the 60th percentile value is 27

i = (p/100 )*n
= (70/100)*8
= 5.6

The index value is not an integer. Round 5.6 to 6. The value is the 6th value in the sorted data set.

Therefore, the 70th percentile value is 28