Explain and discuss central tendency, and the mean. Include an explanation as to how they relate.

Question

What will be an ideal response?

Answer 1

Ans: The most common way to summarize a distribution of scores is to provide a single number that is typical of all scores in the distribution. We call this number a measure of central tendency. In statistics, we use the term average to mean central tendency. Although statisticians use the word average synonymously with central tendency, in everyday use, the term average means the arithmetic mean. However, the arithmetic mean in just one of three commonly used measures of central tendency. The other two are the median and the mode. The most common measure of central tendency is the arithmetic mean, which is the sum of all scores in a set divided by the number of scores in the set. The median divides an ordered set of numbers into two groups of the same size; half of the scores are above the median and half of the scores are below the median. The mode is the most frequently occurring score in a distribution.
The mean is the most frequently used measure of central tendency for quantitative variables. However, the median is more appropriate when the distribution of scores is skewed; income is the classic example of a skewed distribution. The mode is most often used for qualitative variables. It is possible to define the mode for both quantitative and qualitative variables, whereas the mean and the median can be determined only for quantitative variables.