Enter the lower limit of the first quartile group, total number of data points, cumulative frequency of the group before the first quartile group, and the width of the quartile group into the calculator to determine the first quartile.
First Quartile Formula
The following formula is used to calculate the first quartile (Q1) in a data set.
Q1 = L + (N/4 - F) * h
Variables:
- 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
To calculate the first quartile, divide the total number of data points by 4 and subtract the cumulative frequency of the group before the first quartile group. Multiply the result by the width of the quartile group. Add this result to the lower limit of the first 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.
How to Calculate First Quartile?
The following steps outline how to calculate the First Quartile using the given formula:
- First, determine the lower limit of the first quartile group (L).
- Next, determine the total number of data points (N).
- Next, determine the cumulative frequency of the group before the first quartile group (F).
- Next, determine the width of the quartile group (h).
- Finally, calculate the First Quartile (Q1) using the formula: Q1 = L + (N/4 – F) * h.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Lower limit of the first quartile group (L) = 10
Total number of data points (N) = 50
Cumulative frequency of the group before the first quartile group (F) = 20
Width of the quartile group (h) = 5
