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## SOCIAL STATISTICS

Renáta Németh, Dávid Simon

ELTE

Interquartile range

## Interquartile range

but

is based on the maximum and minimum values only, hence it is sensitive to the outliers.

Interquartile range (IQR) is introduced to avoid this instability:

IQR is defined as the difference between the lower and upper quartiles.

Appropriate for interval-ratio variables. (The case of ordinal variables will be discussed later).

Back to the previous example:

 Party preference 1. quartile 3. quartile IQR Range MDF 74250 500000 425.750 457.000 SZDSZ 50750 112500 61.750 476.000 FKGP 47500 68500 21.000 30.000 MSZP 53000 95000 42.000 490.000 FIDESZ 44500 90000 45.500 485.000 Munkáspárt 49100 113750 64.650 87.600 MIÉP 32851 396250 363.399 477.000 Other 56500 218750 162.250 446.000 Uncertain 46000 110000 64.000 498.000 Total 49.250 100.000 50.750 498.000

Check the computation of the IQR by comparing the 3. and 1. quartiles.

Interpret the IQRs!

When variability was measured by the range, uncertain voters showed the highest variability. Has this conclusion changed? How could you explain the change?

Example

Range or IQR? Number of cars within two groups of people.