To find the first quartile (Q1), second quartile (median, Q2), and third quartile (Q3) of this data, follow these steps:

Step 1: Arrange the data in ascending order.

Arranging the numbers in increasing order: 13.80, 13.85, 14.15, 14.30, 14.60, 15.10, 15.15, 15.20, 15.25, 15.25, 15.40, 15.60, 15.80, 15.95, 16.25, 16.30, 16.50, 17.50, 17.55, 17.70, 18.45, 18.70, 19.00, 19.05, 19.40.

Step 2: Count the total number of values.

The dataset contains 25 values.

Step 3: Identify Q1, Q2, and Q3.

1. Median (Q2): The middle value of the dataset.

   • Since the dataset has an odd number of values (25), the median is the 13th value.
   • Median (Q2) = 15.95.

2. First quartile (Q1): The median of the lower half of the dataset (values before Q2).

   • The lower half contains 12 values: 13.80, 13.85, 14.15, 14.30, 14.60, 15.10, 15.15, 15.20, 15.25, 15.25, 15.40, 15.60.
   • The median of these 12 values is the average of the 6th and 7th values: $Q1 = \frac{15.10 + 15.15}{2} = 15.125.$

3. Third quartile (Q3): The median of the upper half of the dataset (values after Q2).

   • The upper half contains 12 values: 15.95, 16.25, 16.30, 16.50, 17.50, 17.55, 17.70, 18.45, 18.70, 19.00, 19.05, 19.40.
   • The median of these 12 values is the average of the 6th and 7th values: $Q3 = \frac{17.55 + 17.70}{2} = 17.625.$

Final Results:

• Q1 = 15.125
• Q2 (Median) = 15.95
• Q3 = 17.625

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Would you like detailed explanations of quartile calculations or further assistance?

Here are 5 related questions you might explore:

1. What is the interquartile range (IQR) of this dataset?
2. How can you visualize these quartiles using a box plot?
3. What do quartiles indicate about data distribution?
4. How would the quartiles change if an additional value was added to the dataset?
5. How are quartiles used in detecting outliers?

Tip: For large datasets, sorting data and calculating quartiles can be simplified using statistical software or programming tools like Excel, Python, or R.