First Quartile Calculator

Formula

The formula to calculate the first quartile (Q1) in a data set is:

\[ Q1 = L + \left(\frac{N}{4} - F\right) \times h \]

Where:

Q1 is the first quartile
L is the lower limit of the first quartile group
N is the total number of data points
F is the cumulative frequency of the group before the first quartile group
h is the width of the quartile group

What is a First Quartile?

The first quartile, also known as the lower quartile or Q1, is a statistical measure that represents the 25th percentile of a data set. This means that 25% of the data points in the set are less than or equal to the first quartile value. It is a type of quantile and is commonly used in descriptive statistics to provide a measure of dispersion and to identify potential outliers. It is calculated by arranging the data in ascending order and finding the median of the lower half of the data.

Example Calculation

Example 1:

Lower Limit (L): 10
Total Number of Data Points (N): 40
Cumulative Frequency (F): 5
Width of Quartile Group (h): 2

Step 1: Calculate the first quartile:

\[ Q1 = 10 + \left(\frac{40}{4} - 5\right) \times 2 = 10 + (10 - 5) \times 2 = 10 + 10 = 20 \]

Example 2:

Lower Limit (L): 15
Total Number of Data Points (N): 60
Cumulative Frequency (F): 10
Width of Quartile Group (h): 3

Step 1: Calculate the first quartile:

\[ Q1 = 15 + \left(\frac{60}{4} - 10\right) \times 3 = 15 + (15 - 10) \times 3 = 15 + 15 = 30 \]