Quartiles divide a sample into four nearly equal pieces. In general, a sample of size n can be broken into knearly equal pieces by using the cutpoints (i / k) (n+1) for i = 1,…., k − 1. Consider the following ordered sample:

2 18 23 41 44 46 49 61 62 74 76 79 82 89 92 95

a. Tertiles divide a sample into thirds. Find the tertiles of this sample.

b. Quintiles divide a sample into fifths. Find the quintiles of this sample.

Step 1 of 3:

It is given that a sample of size n can be divided into k nearly equal parts using the cutpoints

(n+1) ;i=1,2,....,k-1.

Also the given ordered sample is 2,18,23,41,44,46,49,61,64,74,76,79,82,89,92,95.

We have to find the tertiles and quintiles of the sample.

Step 2 of 3:

(a)

Here we have to find the tertiles of the sample. That is we have to divide the sample into three parts.

It is given that the cutpoints to broke the sample is (n+1) ;i=1,2,....,k-1.Here n is 16 and k=3.

Thus the first tertile is given by,

(n+1) =(16+1)

=

=5.67

Thus the first tertile value is the value between 5th and 6th observation in the ordered sample. That is,the first tertile is the average of 5thy and 6th values.It becomes,

=

=45

The second tertile value is obtained by substituting i=2 in (n+1).

That is,

(n+1) = (16+1)

=*17

=

=11.33

Thus the second tertile value is value between 11th and 12th observation in the ordered sample.

Thus the second tertile value is =

=77.5

Thus the first tertile is 45 and the second tertile is 77.5.