# Nonoverlapping Class Intervals into Overlapping Class Intervals

We will learn here how to convert nonoverlapping class intervals into overlapping class intervals.

Conversion of Nonoverlapping Class intervals into Overlapping Class intervals:

If the nonoverlapping class intervals are a - b, c - d, e - f, etc., the gaps between the consecutive class intervals are c - b, e - d, etc. Half of these are $$\frac{c - b}{2}$$, $$\frac{e - d}{2}$$, etc.

The nonoverlapping intervals when changed into overlapping intervals will be (a - $$\frac{c - b}{2}$$) - (b + $$\frac{c - b}{2}$$), (c - $$\frac{c - b}{2}$$) - (d + $$\frac{e - d}{2}$$), etc.

For example:

Nonoverlapping intervals 5 – 9 , 10 – 15, 17 – 23, 26 – 33, etc., when changed into overlapping intervals become (5 - $$\frac{1}{2}$$) - (9 + $$\frac{1}{2}$$), (10 - $$\frac{1}{2}$$) - (15 + $$\frac{2}{2}$$), (17 - $$\frac{2}{2}$$) - (23 + $$\frac{3}{2}$$), etc., that is 4.5 – 9.5, 9.5 – 16, 16 – 24.5, etc.

Nonoverlapping intervals 6 – 15 , 16 – 25, 26 – 35, 36 – 45, etc., when changed into overlapping intervals become (6 - $$\frac{1}{2}$$) - (15 + $$\frac{1}{2}$$), (16 - $$\frac{1}{2}$$) - (25 + $$\frac{1}{2}$$), (26 - $$\frac{1}{2}$$) - (35 + $$\frac{1}{2}$$), etc., that is 5.5 – 15.5, 15.5 – 25.5, 25.5 – 35.5, etc.