Question

Explain the importance of understanding the dispersion of a set of scores in addition to the average score. Give one example from this simulation and one example you can envision.

Answer 1

A measure of spread, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population. It is usually used in conjunction with a measure of central tendency, such as the mean or median, to provide an overall description of a set of data.

There are many reasons why the measure of the spread of data values is important, but one of the main reasons regards its relationship with measures of central tendency. A measure of spread gives us an idea of how well the mean, for example, represents the data. If the spread of values in the data set is large, the mean is not as representative of the data as if the spread of data is small. This is because a large spread indicates that there are probably large differences between individual scores. Additionally, in research, it is often seen as positive if there is little variation in each data group as it indicates that the similar.

Example : range, inter quartile range, standard deviation, variance are important measures of dispersion.

RANGE : The range is the difference between the highest and lowest scores in a data set and is the simplest measure of spread. So we calculate range as:

Range = maximum value - minimum value

For example, let us consider the following data set:

23 56 45 65 59 55 62 54 85 25

The maximum value is 85 and the minimum value is 23. This results in a range of 62, which is 85 minus 23. Whilst using the range as a measure of spread is limited, it does set the boundaries of the scores. This can be useful if you are measuring a variable that has either a critical low or high threshold (or both) that should not be crossed. The range will instantly inform you whether at least one value broke these critical thresholds. In addition, the range can be used to detect any errors when entering data. For example, if you have recorded the age of school children in your study and your range is 7 to 123 years old you know you have made a mistake!

VARIANCE :

You and your friends have just measured the heights of your dogs (in millimetres):The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

To calculate the Variance, take each difference, square it, and then average the result:

Mean = 600 + 470 + 170 + 430 + 3005

= 19705

= 394

Variance

σ2 = 2062 + 762 + (−224)2 + 362 + (−94)25

= 42436 + 5776 + 50176 + 1296 + 88365

= 1085205

= 21704

So the Variance is 21,704

As the variance is high we conclude there is huge variability aming the heights of the dogs.