Find the third quartile from the following list of data.
5.3, 6.2, 8.4, 9.1, 13.0, 15.7, 18.2, 19.4, 22.0, 25.0

To find the third quartile (Q3) in a dataset, we need to first ensure the data is ordered, then identify the value that separates the highest 25% of values from the rest.

Here's the ordered data set:
5.3, 6.2, 8.4, 9.1, 13.0, 15.7, 18.2, 19.4, 22.0, 25.0

Since there are 10 data points, the formula for finding \( Q3 \) is:

\[
Q3 = \text{value at } \left(\frac{3(n+1)}{4}\right)^{th} \text{ position}
\]

where \( n \) is the number of data points. Substituting \( n = 10 \):

\[
Q3 = \text{value at } \left(\frac{3(10+1)}{4}\right)^{th} \text{ position} = \text{value at } \left(\frac{33}{4}\right)^{th} \text{ position} = \text{value at } 8.25^{th} \text{ position}
\]

Since the 8.25th position is between the 8th and 9th data points (19.4 and 22.0), we can interpolate between them:

\[
Q3 = 19.4 + (0.25)(22.0 - 19.4) = 19.4 + 0.65 = 20.05
\]

**So, the third quartile (Q3) is approximately 20.05.**

Would you like further details, or do you have any questions?

### Related Questions:
1. How do you find the first quartile (Q1) for this data set?
2. What is the interquartile range (IQR) of this data?
3. How does the formula for quartiles change for different data set sizes?
4. What does it mean if a data point lies above the third quartile?
5. How would you calculate the median (Q2) for this data set?

### Tip:
Quartiles are useful for understanding the spread and distribution of data, especially when analyzing large data sets.

Find the third quartile from the following list of data. 5.3, 6.2, 8.4, 9.1, 13.0, 15.7, 18.2, 19.4, 22.0, 25.0

Discover how to calculate the third quartile (Q3) for the data set 5.3, 6.2, 8.4, 9.1, 13.0, 15.7, 18.2, 19.4, 22.0, 25.0. Learn the step-by-step process for finding Q3, including interpolation methods for datasets with even numbers of values. Suitable for high school students in Grades 10-12.

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