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.

9th Grade Math

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