1. Meaning of Quartiles
Quartiles divide the data into four equal parts when the values are arranged in ascending order. They help understand how the data is spread around the center.
- Q1 (First Quartile): The value below which 25% of the data lies.
- Q2 (Second Quartile): The median; 50% of the data lies below it.
- Q3 (Third Quartile): The value below which 75% of the data lies.
The difference between Q1 and Q3 tells how widely the middle half of the data is spread.
2. Meaning of Quartile Deviation
Quartile deviation (also called the semi-interquartile range) measures the spread of the middle 50% of the data. It is less affected by extreme values because it focuses only on values around the center.
It tells how far, on average, the middle values move away from the center of the distribution.
3. Formula for Quartile Deviation
The formula for quartile deviation is:
\( QD = \dfrac{Q3 - Q1}{2} \)
Here:
- \( Q1 \) = first quartile
- \( Q3 \) = third quartile
4. Steps to Calculate Quartile Deviation
- Arrange the data in ascending order.
- Find the positions of Q1 and Q3.
- Determine the values of Q1 and Q3.
- Use the formula \( QD = \dfrac{Q3 - Q1}{2} \).
5. Example
Consider the data: 4, 7, 10, 12, 15, 18, 20
Step 1: Arrange — already arranged
Step 2: Q1 is the value at one-quarter position:
\( Q1 = 7 \)
Step 3: Q3 is the value at three-quarter position:
\( Q3 = 18 \)
Step 4: Apply formula:
\( QD = \dfrac{18 - 7}{2} = \dfrac{11}{2} = 5.5 \)
So, the quartile deviation is 5.5.