Range = (Maximum - Minimum) = (29500 - 2200) = 27300

All Commodores |
Omitting $29,500 |
||
---|---|---|---|

Median | 9,500 | 9,500 | not changed |

Max | 29,500 | 20,000 | changed |

Min | 2,200 | 2,200 | |

Range | 27,300 | 17,800 | changed greatly |

Mean | 10,080 | 9,555 | changed |

The range depends only on the extreme values in the data set.

Mistakes in data, such as reversing digits (e.g. 52 for 25) or omitting
digits (e.g. 12 for 132) may produce extreme values. A measure of the spread
of data which is not so much affected by extreme values as the range is
to take values 5% in from either end, or 1/4 in from either end.

When the data are arranged in order of magnitude (i.e. they are ranked) the quartiles are 3 numbers which divide the data into four groups each having approximately the same number of values.

- Order the n data values from smallest to largest.
- The 2nd quartile, Q
_{2}is the median of the whole data set. - If n is even, the first quartile, Q
_{1}, is the median of the smallest n/2 observations and the third quartile, Q_{3}, is the median of the largest n/2 observations. - If n is odd, Q
_{1}is the median of the smallest observations, and Q_{3}is the median of the largest obesrvations.

EXAMPLE. Consider first 9 Commodore prices ( in $,000)

Arrange these in order of magnitude

The median is Q_{2} = 6.7 (there are 4 values on either
side)

Q_{1} = 5.9 (median of the 4 smallest values)

Q_{3} = 10.2 (median of the 4 largest values)

IQR = 10.2 - 5.9 = 4.3.

[Some textbooks and computer programs use slightly different definitions
for Q_{1} and Q_{3} from the ones given here. The
calculated values, however, are usually very similar. Use HELP DESCRIBE
to see the MINITAB definition.]

Just as the median is not affected much by extreme values, neither is the IQR. For example, for the Commodore prices MINITAB gives

The percentiles most commonly used, after the 50th, are those close to 100. Thus the 90th percentile is the value that is exceeded by only 10% of the sample or the population, and the 99th percentile is exceeded by only 1 in 100.

You will occasionally also see "deciles", which are found by dividing the data into tenths, and "quintiles", which divide the data into fifths. The first quintile is identical to the 20th percentile, the median is the fifth decile, and so on.

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