15 Quartiles divide a sample into four nearly equal pieces I

15. Quartiles divide a sample into four nearly equal pieces. In general. a sample of size n can be broken into k nearly equal pieces by using the cut points (1 / k) (n + 1) for ? = 1, . . . . k ? 1. Consider the following ordered sample: 2 182341 44 464961 62 74 76 79 82 89 92 95 a. Tertiles divide a sample into thirds. Find the tenues of this sample. b. Quintiles divide a sample into fifths. Find the quintiles of this sample.

Solution

Part (a)

The tertiles divide the sample into thirds i.e. into three equal parts

Step 1

Layout the series in ordered sequence

Here it is an already ordered sequence

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

The formula for thefirst tertile is: (n+1)/k and that for the second tertile is 2(n+1)/k where k=3 and n=16

or 5.67 th term would be the first tertile and second tertile is the 11.34th trem of the sample.

here elimination of 2 from the sample would generate effective results which can be subjected to analysis.

that done the first tertile becomes the 6th observation-46 and the second tertile becomes the 11th observation-76

Part (b)

Similarly the quintiles would be the

3.2th, 6.4th, 9.6th and 12.8th observations.

Through extrapolation we get the values from the sample.