The purpose of this memorandum is to give some insight on what are some methodologies and applications that relate to the different levels of measurement, central tendency, dispersion, and some other key statistical metrics in regards to data that was attained from the AMA website for zip code 60614 out of Illinois.
There are two characteristics of a frequency distribution that are very important when it comes to giving a summary of data. This also involves making predictions per se from one set of results to another. In fact, central tendency labels things such as: what is in the middle of this data, what is most common about this data, and what would this data be used to predict. This relates to the mean, median which the median is the most suitable measure of central tendency for ordinal data, although it is also widely used with interval/ratio variables. It is simply the middle value in a distribution when the scores are ranked in order of size, and that of the mode, which is the simplest measure of central tendency to calculate and is the only measure that is the most appropriate for nominal data. The mode is the value that occurs most frequently in a distribution. On the other hand, dispersion actually tells things such as: how spread out is this data that we are working with, and the shape that the data might be (Palgrave, 2009). The three measures of central tendency are commonly used in statistical analysis – the mode, the median, and the mean with each of these measures designed to represent a certain score. This actually depends on the shape of the distribution (whether normal or skewed), and the variable’s “level of measurement” (data are nominal, ordinal or interval).
Dispersion deals with things such as range, which is the most straightforward measure of dispersion and is calculated by subtracting the smallest value from the largest. It is the key concept in statistical thinking. Standard deviation which, the most widely used measure of dispersion and is obtained by simply calculating the square root of the variance. As this returns us to the original unit of measurement the standard deviation is much more meaningful than the variance. If the mean is being used as the measure of central tendency it is usually accompanied by the standard deviation. It is important to be aware that because the standard deviation, like the mean, is calculated using all the observations it can be distorted by a small number of extreme values. The variance and standard deviation tell us how widely dispersed the values in a distribution are around the mean. Like the mean they require variables to be measured on the interval/ratio scale. If the values are closely concentrated around the mean the variance will be small, while a large variance suggests a batch of values which are much more dispersed (Palgrave, 2009).
Level of measurement focuses on things such as types of data that are nominal, ordinal, or interval and ratio data. Nominal data is where you use numbers to classify data. Then there is ordinal data which is where values are given to measurements can be ordered. Interval data is that which is where measurements are not only classified and ordered therefore having the properties of the two previous scales, but the distances between each interval on the scale are equal right along the scale from the low end to the high end. And the ratio data is that which it can be expressed on a ratio scale can have an actual zero. Apart from this difference, ratio scales have the same properties as interval scales. The divisions between the points on the scale have the same distance between them and numbers on the scale are ranked according to size (Wharrad, 2004).
References:
Palgrave, (2009). Central Dependency, Dispersion, and Levels of Measure. Retrieved on January 21, 2012 from http://www.palgrave.com
Wharrad, H., (2004). Levels of Measurement. Retrieved on January 21, 2012 from http://www.ucel.ac.uk/showroom/levels_of_measurement/