To find the third quartile (Q3) of the data set, we follow these steps:

Step 1: Arrange the data in ascending order.

First, we list all the numbers in order from smallest to largest:

36, 36, 37, 38, 39, 39, 39, 40, 40, 40,
40, 41, 41, 41, 41, 41, 42, 42, 42, 42,
43, 43, 44, 44, 44, 44, 45, 45, 45, 47,
48, 48, 48, 48, 50, 54, 60

Step 2: Determine the position of Q3.

The third quartile (Q3) is the median of the upper half of the data. Since there are 37 data points, Q3 will be at the position $\frac{3(n+1)}{4}$.

Where $n = 37$, so the position is:

$\frac{3(37 + 1)}{4} = \frac{3(38)}{4} = \frac{114}{4} = 28.5$

This means Q3 is between the 28th and 29th data points.

Step 3: Find the value of Q3.

From the ordered data set:

• The 28th data point is 45.
• The 29th data point is 47.

Since Q3 is between these two points, we average them:

$Q3 = \frac{45 + 47}{2} = \frac{92}{2} = 46$

Final Answer:

The third quartile (Q3) is 46.

Would you like further details or have any questions about this process?

Here are 5 related questions you might find interesting:

1. What is the first quartile (Q1) of this data set?
2. How do you calculate the interquartile range (IQR)?
3. What is the median (Q2) of this data set?
4. How can outliers be detected using quartiles and IQR?
5. What is the range of this data set?

Tip: Quartiles divide a data set into four equal parts, providing a good measure of spread and central tendency.