5.2.1 The Range

Of all the measures of variability, the range is the easiest and quickest way to determine. It is simply the difference of the highest (H) and the lowest (L) scores in a set of data under consideration.

Formula for the Range:

r = H – L

where: r = range H = highest score L = lowest score

Example:The scores of Maria in her math quizzes are as follows: 12, 25, 27, 29, 36, 38, 40, 43, 50, and 62. Find its range.

Solution: Highest score (H) = 62 Lowest score (L) = 12

r = H – L = 62 – 12 = 50

Therefore, the range is 50.

5.2.1.1 Other Characteristics of the

Range

AdvantagesGIVES QUICK APPROXIMATION OF

THE VARIABILITY OF DATA.IT IS NOT VERY

SOPHISTICATED/COMPLICATED.USED WHEN THE MODE IS

PREFERRED MEASURE OF CENTRAL TENDENCY. (I.E./ WHEN YOU HAVE NOMINAL/TITULAR LEVEL DATA.)IT IS THE SIMPLEST MEASURE OF

VARIABILITY/DISPERSION.

Disadvantages

It is limited/partial, if extreme scores are not representative of the sample, but are included among the scores.

It is not very informative, because it is based only on the most extreme scores.

It is severely affected by extreme scores in your data distribution.

5.2.2 The Average Deviation

The average deviation is the “average” amount each score deviates/differs from the mean. It is always zero, as a consequence of one of the properties of the mean (that the sum of the deviations about the mean is zero ). It cannot be calculated without first calculating the mean.

Consequently, the mean deviation is usually expressed as the mean of the absolute values of the deviations from the mean. That is why it is also called the Mean Absolute Deviation (M.A.D.).

5.2.3.3 Characteristics of the Inter-Quartile Range of the

Quartile Deviation

1. It is less likely influenced by extreme scores, therefore, giving a better and stable measure of variability than the range.

2. It discards/removes too much of the data. It does not give a complete picture of the variability.

3. The mean and mean absolute deviation are both affected by outliners and may not be good representations of the data in cases where outliners are alike. In these cases, the median and the interquartile range/Q.D. may be a better choice.

4. The IQR is a nice measure to use if one wishes to do short numerical description of a data set. It is resistant to the effects of outliners, but it has the significant disadvantage of not being easily analyzed. One of the uses of the IQR is in the identification of outliners.

5.The Semi-Interquartile Range or the Q.D. is used when the median is the referred measure of the central tendency (i.e., with ordinal level or skewed data)