what is the best measure of central tendency is with respect to the different types of variable and when to use the mean, median and mode in data analysis

Measures of Central Tendency
A measure of central tendency is a single value that attempts to describe a set of data by
identifying the central position within that set of data. As such, measures of central tendency
are sometimes called measures of central location. They are also classed as summary
statistics. The mean (often called the average) is most likely the measure of central tendency
that you are most familiar with, but there are others, such as the median and the mode. The
mean, median and mode are all valid measures of central tendency, but under different
conditions, some measures of central tendency become more appropriate to use than others.
Arithmetic Mean
The mean (or average) is the most popular and well known measure of central tendency. It
can be used with both discrete and continuous data, although its use is most often with
continuous data. The mean is equal to the sum of all the values in the data set divided by the
number of values in the data set. So, if we have n values in a data set and they have values x1,
x2, ..., xn, the sample mean, usually denoted by (pronounced x bar), is:
This formula is usually written in a slightly different manner using the Greek capitol letter, ,
pronounced "sigma", which means "sum of...":
An important property of the mean is that it includes every value in your data set as part of
the calculation. In addition, the mean is the only measure of central tendency where the sum
of the deviations of each value from the mean is always zero.
When not to use the mean
The mean has one main disadvantage: it is particularly susceptible to the influence of outliers.
These values are unusual compared to the rest of the data set by being especially small or
large in numerical value. For example, consider the wages of staff at a factory below:
Staff 1 2 3 4 5 6 7 8 9 10
Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k...