Let's go through the process of finding the third quartile (Q3) for your sample of 14 numbers:

Given numbers:

3.1, 4, 4, 4, 5.8, 5.9, 6, 8, 12, 13, 14.7, 15, 15, 15

Step 1: Arrange the numbers in ascending order (already sorted):

3.1, 4, 4, 4, 5.8, 5.9, 6, 8, 12, 13, 14.7, 15, 15, 15

Step 2: Find Q2 (the median): Since the number of data points is 14 (even), the median (Q2) is the average of the 7th and 8th values in the sorted list:

• 7th value: 6
• 8th value: 8

So, Q2 = $\frac{6 + 8}{2} = 7$.

Step 3: Find Q1 (the first quartile): Q1 is the median of the lower half of the data, excluding the median. The lower half consists of the first 7 numbers:

3.1, 4, 4, 4, 5.8, 5.9, 6

The median of these 7 values is the 4th value, which is 4. Therefore, Q1 = 4.

Step 4: Find Q3 (the third quartile): Q3 is the median of the upper half of the data, excluding the median. The upper half consists of the last 7 numbers:

8, 12, 13, 14.7, 15, 15, 15

The median of these 7 values is the 4th value, which is 14.7. Therefore, Q3 = 14.7.

Answer:

• Q1 = 4
• Q2 = 7
• Q3 = 14.7

Would you like further explanation on how quartiles are calculated, or do you have any other questions on this?

Here are 5 related questions:

1. How do you find the interquartile range (IQR)?
2. What does Q3 represent in a data set?
3. How is the median calculated for an odd number of data points?
4. How do you handle outliers when calculating quartiles?
5. What is the significance of quartiles in data analysis?

Tip: When working with quartiles, always ensure that your data is sorted in ascending order before calculating the medians for each quartile.