# Strengths and weaknesses of the measures of central tendency and dispersion

Mean, Median and Mode The mean, median and mode are all measures of central tendency. Central Tendency- Descriptive statistics that identify which value is most typical for the data set The Mean Adding all of the scores in a data set together and dividing by the number of scores. The most powerful measure of central tendency because it it made up from all of the scores in the data set Disadvantages: Any rogue outliers can distort the mean making it untypical of the data set Sometimes the mean does not make sense in terms of the data set e. Agree Strongly Agree If two people rate a question as a 4 that does not mean that they have anywhere near the same sense of "agreement" with the question.

Even the same person may mark two questions with a 4 and feel quite different about the actual extent of agreement with the two statements. Finding the mean of ordinal values does not make sense, and it should not be done. Please be aware of the fact that few people understand the absurdity and inappropriateness of calculating the mean for ordinal values.

In fact, finding such a mean is done all the time. Opinion surveys are given, results are scanned and coded, and the data is fed into computer programs that automatically calculate the mean of the data set.

Then the results are studied and even published. The ease of doing a computation should not be confused with the appropriateness of doing it. The computer programs do not ask for the kind of data. Those programs are more than happy to compute the mean for any kind of data. It is the task of the responsible user to know the kind of data being studied, and the appropriate measures to use for that data.

When interval and ratio measures were introduced in an earlier section we noted that there is a degree of accuracy associated with these kinds of measurements. Finding the mean of interval and ratio measures produces a value that could easily be one of the measurements.

It would make sense to find that the mean height of female math students is There is no color assigned to that value. We had 4 as a blue and 5 as a light brown. The mean is not a color "between" these two.

In the same way, to find that the mean response of students to an opinion survey statement is 3. The mean is a powerful measure of central tendency for interval and ratio measurements. However, the mean is not without its problems.

The value that we compute as the mean of a set of data can be highly influenced by extreme values in that data. This is especially true for small data sets or even for larger ones if the extreme values are outrageously extreme.

Let us demonstrate this. All of the values in that data set are at least close to the mean, and one gets the feeling that the mean, 8, is representative of the numbers in the data set. Let us see what happens to the mean if we change just one value to be much more extreme, that is, to be far away from the rest of the values.Measures of. Variability. CHAPTER. 4.

Chapter Outline. An Example From the. The Range • Strengths and weaknesses of the range The Interquartile Range • Strengths and weaknesses of the interquartile range Similar to measures of central tendency, there are multiple measures.

o What does this exercise indicate about the strengths and weaknesses of each of the measures of central tendency? o Calculate the range . The measures of central tendency are the mean, the median, and the mode.

These values are computed from the data that we are given. These values are computed from the data that we are given. The mean and median are two different attempts to find a single number to represent the "center" of the data values.

A measure of central tendency is a single value that describes the way in which a group of data cluster around a central value. To put in other words, it is a way to describe the center of a data set. CENTRAL TENDENCY. Central tendency is defined as “the statistical measure that identifies a single value as representative of an entire distribution.”[] It aims to provide an accurate description of the entire grupobittia.com is the single value that is most typical/representative of the collected data.

What are the strengths and weaknesses of Mean, median and mode? Mean. median, mode and standard deviation are all what we call measures of central tendency. All have some value, and I would teach students to do all four measures for any data set.

Also the natural measure of dispersion associated with the mean is the mean absolute.

Statistical Language - Measures of Central Tendency