Calculating Quartile Deviation
To calculate the quartile deviation for the given data set, we first need to find the first and third quartiles. The quartile deviation is a measure of statistical dispersion and is calculated as the difference between the first and third quartiles.

Calculating Quartiles
- Start by arranging the data in ascending order: 2, 3, 4, 4, 5, 6
- Calculate the position of the first quartile (Q1) using the formula: (n+1)/4 = (6+1)/4 = 1.75
- Since 1.75 is not a whole number, we take the average of the values at positions 1 and 2: (2+3)/2 = 2.5
- Q1 is 2.5
- Calculate the position of the third quartile (Q3) using the formula: 3(n+1)/4 = 3(6+1)/4 = 5.25
- Again, since 5.25 is not a whole number, we take the average of the values at positions 5 and 6: (5+6)/2 = 5.5
- Q3 is 5.5

Calculating Quartile Deviation
- Quartile deviation = (Q3 - Q1)/2 = (5.5 - 2.5)/2 = 1.5
Therefore, the quartile deviation for the given data set is 1.5. This means that the middle 50% of the data values lie within 1.5 units of each other, providing a measure of the spread or dispersion of the data.