To find the quartiles using the Tukey method, follow these steps:

Step 1: Organize the data in ascending order

We are given the following data set of customer ages:

$20, 33, 34, 29, 30, 32, 31, 13, 29, 11, 36, 23, 43, 48, 25, 26, 23, 32, 35, 33, 36, 43, 44, 43, 47$

First, sort these values in ascending order:

$11, 13, 20, 23, 23, 25, 26, 29, 29, 30, 31, 32, 32, 33, 33, 34, 35, 36, 36, 43, 43, 43, 44, 47, 48$

Step 2: Calculate the Quartiles using the Tukey Method

• Q1 (First Quartile): This is the median of the lower half of the data, not including the median of the entire dataset.
• Q3 (Third Quartile): This is the median of the upper half of the data.

Since there are 25 data points, the median (Q2) is the 13th value.

Lower Half of the Data (for Q1):

The lower half includes the first 12 data points: $11, 13, 20, 23, 23, 25, 26, 29, 29, 30, 31, 32$

To find Q1, take the median of these 12 numbers. The middle two values are 25 and 26, so:

$Q1 = \frac{25 + 26}{2} = 25.5$

Upper Half of the Data (for Q3):

The upper half includes the last 12 data points: $33, 33, 34, 35, 36, 36, 43, 43, 43, 44, 47, 48$

To find Q3, take the median of these 12 numbers. The middle two values are 36 and 43, so:

$Q3 = \frac{36 + 43}{2} = 39.5$

Conclusion:

Using the Tukey method:

• $Q1 = 25.5$
• $Q3 = 39.5$

Would you like further details on quartiles or Tukey's method?

Related Questions:

1. How are quartiles used to identify outliers in a data set?
2. What is the Interquartile Range (IQR), and how can it be calculated from quartiles?
3. How does the Tukey method differ from other methods of calculating quartiles?
4. Can you explain how box plots visually represent quartiles?
5. How can the quartiles help in analyzing the spread of the data?

Tip: Always sort your data before calculating quartiles to ensure accuracy.