Q.In the above example, minimum hight value is 85 cm and maximum hight value is 115 cm.

Suppose you have the marks of a hundred students and you want a picture of how they are spread. Listing all hundred numbers tells a reader nothing. Instead you group them into bands — 0 up to 10, 10 up to 20, and so on — and count how many students fall in each band. Each band is a class interval, and the width of a band (how much of the number line it covers) is the interval width. Choosing that width sensibly is what makes a frequency table or a histogram readable.

The reasoning runs in three steps:

• First find the range of the data: the distance from the smallest value to the largest (highest minus lowest). This is the total stretch of number line your intervals must cover between them.
• Decide how many intervals you want. For classroom-sized data, somewhere between five and ten intervals usually gives a useful picture.
• The width of each interval is then the range divided by the number of intervals, rounded up to a convenient figure so the bands have clean boundaries (widths of 5 or 10 rather than 7.3).

The trade-off behind the choice is the real concept. Make the intervals too wide and you get very few bars, each swallowing so many students that all detail vanishes — the histogram becomes a blur. Make them too narrow and you get dozens of bars with one or two students each — the histogram becomes noise. The right width is the one that shows the shape of the data: where the bulk sits, whether it leans left or right, whether there are two humps. …