The formula to calculate the first quartile (Q1) in a data set is:
\[ Q1 = L + \left(\frac{N}{4} - F\right) \times h \]
Where:
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 1:
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:
Step 1: Calculate the first quartile:
\[ Q1 = 15 + \left(\frac{60}{4} - 10\right) \times 3 = 15 + (15 - 10) \times 3 = 15 + 15 = 30 \]
