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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