first quartile

What is the First Quartile in Math? Definition

The first quartile, also known as Q1 or the lower quartile, is a statistical measure used in mathematics to divide a dataset into four equal parts. It represents the value below which 25% of the data falls. In other words, it is the median of the lower half of the dataset.

History of First Quartile

The concept of quartiles dates back to the 19th century when Francis Galton introduced the idea of dividing a dataset into four equal parts. Quartiles gained popularity in the field of statistics and have since become an essential tool for analyzing data distributions.

What Grade Level is First Quartile For?

The concept of quartiles is typically introduced in middle or high school mathematics courses. It is commonly covered in statistics or data analysis units, where students learn about measures of central tendency and data distribution.

Knowledge Points of First Quartile and Detailed Explanation Step by Step

To find the first quartile, follow these steps:

1. Arrange the dataset in ascending order.
2. Calculate the position of the first quartile using the formula: (n + 1) / 4, where n is the total number of data points.
3. If the position is a whole number, the first quartile is the value at that position.
4. If the position is not a whole number, round it down to the nearest whole number and find the corresponding value in the dataset. This will be the first quartile.

For example, let's consider the dataset: 5, 8, 10, 12, 15, 18, 20, 22, 25, 30.

1. Arrange the dataset in ascending order: 5, 8, 10, 12, 15, 18, 20, 22, 25, 30.
2. Calculate the position of the first quartile: (10 + 1) / 4 = 2.75.
3. Round down the position to 2.
4. The first quartile is the value at position 2, which is 8.

Therefore, the first quartile of the dataset is 8.

Types of First Quartile

There is only one type of first quartile, which represents the lower 25% of the data.

Properties of First Quartile

• The first quartile divides the dataset into two equal parts: the lower 25% and the upper 75%.
• It is resistant to extreme values or outliers in the dataset.
• The first quartile is always less than or equal to the median.

How to Find or Calculate First Quartile?

To find the first quartile, follow the steps mentioned earlier. Arrange the dataset in ascending order, calculate the position using the formula, and find the corresponding value.

Formula or Equation for First Quartile

The formula to calculate the position of the first quartile is: (n + 1) / 4, where n is the total number of data points.

How to Apply the First Quartile Formula or Equation?

To apply the first quartile formula, substitute the value of n (total number of data points) into the formula and calculate the position. Then, use this position to find the corresponding value in the dataset.

Symbol or Abbreviation for First Quartile

The symbol for the first quartile is Q1.

Methods for First Quartile

The main method for finding the first quartile is by calculating its position using the formula and then locating the corresponding value in the dataset.

Solved Examples on First Quartile

Example 1: Consider the dataset: 12, 15, 18, 20, 22, 25, 30, 35, 40, 45. Find the first quartile.

Solution:

1. Arrange the dataset in ascending order: 12, 15, 18, 20, 22, 25, 30, 35, 40, 45.
2. Calculate the position of the first quartile: (10 + 1) / 4 = 2.75.
3. Round down the position to 2.
4. The first quartile is the value at position 2, which is 15.

Therefore, the first quartile of the dataset is 15.

Example 2: Consider the dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22. Find the first quartile.

Solution:

1. Arrange the dataset in ascending order: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.
2. Calculate the position of the first quartile: (11 + 1) / 4 = 3.
3. The first quartile is the value at position 3, which is 6.

Therefore, the first quartile of the dataset is 6.

Example 3: Consider the dataset: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. Find the first quartile.

Solution:

1. Arrange the dataset in ascending order: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
2. Calculate the position of the first quartile: (10 + 1) / 4 = 2.75.
3. Round down the position to 2.
4. The first quartile is the value at position 2, which is 3.

Therefore, the first quartile of the dataset is 3.

Practice Problems on First Quartile

1. Find the first quartile of the dataset: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
2. Calculate the first quartile of the dataset: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33.
3. Determine the first quartile of the dataset: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34.

FAQ on First Quartile

Question: What is the first quartile? The first quartile is a statistical measure that represents the value below which 25% of the data falls. It divides a dataset into four equal parts.

Question: How is the first quartile calculated? The first quartile is calculated by arranging the dataset in ascending order, calculating its position using the formula (n + 1) / 4, and finding the corresponding value.

Question: What is the symbol for the first quartile? The symbol for the first quartile is Q1.

Question: Is the first quartile resistant to outliers? Yes, the first quartile is resistant to extreme values or outliers in the dataset.