Question

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 cutpoints for k-1 quartiles. 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.

Answer 1

The first tertile (T₁) is 23, the second tertile (T₂) is 76, and the third tertile (T₃) is 89.

Step-by-step explanation:

To find the tertiles of the given sample, we need to divide the data into thirds. Since there are 16 values in the sample, we can divide it into 3 groups of roughly equal size. The first tertile (T₁) will be the middle value of the first group, the second tertile (T₂) will be the middle value of the second group, and the third tertile (T₃) will be the middle value of the third group.

When the given sample is arranged in ascending order, the first group will be from 2 to 49, the second group will be from 61 to 82, and the third group will be from 89 to 95. Therefore, the tertiles for this sample are:

• T₁ (First Tertile): 23
• T₂ (Second Tertile): 76
• T₃ (Third Tertile): 89