15, 15, 19, 20, 20, 21, 25, 29 what is Q3

To find \( Q_3 \) (the third quartile), which represents the 75th percentile of the dataset, follow these steps:

1. **Organize the data**: The dataset is already arranged in ascending order:
   \[
   15, 15, 19, 20, 20, 21, 25, 29
   \]
   
2. **Determine the position of \( Q_3 \)**: For a dataset with \( n \) values, \( Q_3 \) is the median of the upper half. First, we need to find the position:
   \[
   Q_3 = \frac{3(n + 1)}{4}
   \]
   Here, \( n = 8 \), so:
   \[
   Q_3 = \frac{3(8 + 1)}{4} = \frac{27}{4} = 6.75
   \]
   This means \( Q_3 \) lies between the 6th and 7th values in the data set.

3. **Locate \( Q_3 \)**: The 6th and 7th values are 21 and 25. To find \( Q_3 \), we calculate:
   \[
   Q_3 = 21 + 0.75 \times (25 - 21) = 21 + 0.75 \times 4 = 21 + 3 = 24
   \]

Thus, \( Q_3 = 24 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How is \( Q_1 \) (the first quartile) calculated in a dataset?
2. What is the interquartile range (IQR) and how is it useful?
3. How does the method change if the dataset has an odd number of elements?
4. What are the uses of quartiles in statistical analysis?
5. How does \( Q_3 \) compare with the maximum value in the dataset?

**Tip**: Quartiles help in understanding the spread and distribution of the data, especially in detecting outliers.

Learn how to calculate the third quartile (Q3) for the dataset 15, 15, 19, 20, 20, 21, 25, 29. This detailed guide explains the step-by-step process, including quartile formulas and how to find the 75th percentile in a data set. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation