To find the first quartile (Q1) of a data set, follow these steps:
- Order the data from smallest to largest.
- Determine the position of Q1 using one of these common methods:
- Using the formula: Q1=n+14Q1=\frac{n+1}{4}Q1=4n+1th term, where nnn is the number of data points. This gives the position of Q1 in the ordered list. If the result is not an integer, round up to the next whole number and take the value at that position as Q1
* Alternatively, multiply the number of data points by 0.25 (25%) to find the position. If this is not a whole number, round up to the next integer to find Q1's position
- Find the median of the lower half of the data (all data points below the overall median). This median of the lower half is Q1. If the number of data points is odd, exclude the overall median when splitting the data into halves
- Interpretation: Q1 represents the value below which 25% of the data fall
Summary Example
- Suppose you have 10 data points sorted in ascending order.
- Calculate (n+1)/4=(10+1)/4=2.75(n+1)/4=(10+1)/4=2.75(n+1)/4=(10+1)/4=2.75. Round up to 3, so Q1 is the 3rd value in the ordered data.
- Alternatively, 0.25 × 10 = 2.5, round up to 3, same result.
- The value at position 3 is Q1.
This method ensures Q1 divides the lowest 25% of data from the rest
. In brief, Q1 is the median of the lower half of the ordered data set, or the data value at the position given by(n+1)/4(n+1)/4(n+1)/4
