Question

Find the first, second, and third quartiles of the data. $$2.3,5.6,3.4,4.5,3.8,1.2,9.7$$

Short answer

The first quartile Q1 = 2.85, the second quartile Q2 = 3.8, and the third quartile Q3 = 5.05.

Step-by-step solution

Arrange the Data

The first step always includes rearranging the data into ascending order. After rearranging the given data, 2.3, 5.6, 3.4, 4.5, 3.8, 1.2, 9.7, obtain the following sequence: 1.2, 2.3, 3.4, 3.8, 4.5, 5.6, 9.7.

Identify Key Points

The next step is to split the arranged data into two halves. Look at the median (the middle value) of our sequence, which is 3.8, as the second quartile (Q2). Now, by splitting the dataset into two halves (excluding the median for an odd number of observations), identify the median of each half as the first (Q1) and third (Q3) quartiles respectively.

Calculate Q1, Q2, and Q3

Observing the first four data points, which are 1.2, 2.3, 3.4, and 3.8, we see that there are only two data points in the middle. Hence, we calculate their average to obtain Q1: Q1 = (2.3 + 3.4) / 2 = 2.85. Doing the same for the final four data points (3.8, 4.5, 5.6, and 9.7), we find that Q3 = (4.5 + 5.6) / 2 = 5.05.