That is, by choosing a set of contiguous non-overlapping intervals, called class intervals, the observations can be grouped to form a discrete variable from the continuous variable.

The following data set will be used to illustrate various concepts and methods.

6000 | 6700 | 3800 | 7000 | 5800 | 9975 | 10500 | 5990 |

20000 | 11990 | 16500 | 10750 | 9500 | 12995 | 12500 | 8000 |

9900 | 18000 | 9500 | 9400 | 7250 | 15000 | 4500 | 8900 |

9850 | 9000 | 5800 | 29500* | 15000 | 9000 | 4250 | 4990 |

11000 | 9990 | 2200 | 4000 | 13500 | 14500 |

* This car was described as 'prototype, exclusive, group A look alike'
(ie similar to cars used for racing).

- Usually use from 5 to 15 intervals.
- Calculate the range and divide it by the chosen number of intervals to get the approximate length for each interval.
- Define interval end points so they don't overlap or leave gaps (ie. they are mutually exclusive and exhaustive) - This ensures that every observation belongs in exactly one interval.
- It is a usually simpler idea to have all intervals of the same length
- Count the number of values in each interval (the class frequency) - go through the data once only and use tally marks to help counting.
- Usually relative frequencies or percentages are helpful to show the distribution of data.

Draw rectangles over each interval so that

**area of rectangle = frequency (or relative frequency)**

But **area = length x height**

So if all intervals are the same length, *L*

Heights are directly proportional to the frequencies only if all intervals are the same length.

For the histogram shown above, for the Commodore prices, the interval "20000 or more" was changed to four intervals, 20000 - 22999, 23000 - 25999, 26000 - 28999, 29000 - 31999 in order to have properly defined endpoints and equal lengths for all intervals.

If intervals are not all of the same length then heights have to be scaled so that each area is proportional to the frequency for that interval.

Note MINITAB rotates the histogram 90 degrees.

Here is another histogram applet, by R. Webster West, Dept. of Statistics, Univ. of South Carolina.

MTB > DotPlot 'price'.

## Progress check |

... Previous page | Next page ... |