in which kind of situations the mode is the best choice? Give example.
Answers
The mode is totally insensitive to outliers, this is a great property when working with very noisy data or where idiossincratic events tend to happen (e.g. Economics or politics).
The drawbacks of the mode are it isn’t unique nor it exists for every distribution.
The mean also has this drawbacks, sometimes it won’t be finite or have a closed form.
The median always exists and it’s insensitive (less than the mode but nonetheless robust) to outliers.
In my view, it will always come down to what’s your objective, if you’re doing theoretical or empirical work. In the later case it will also depend, on the results yielded after doing some exploratory analyses over your data.
For example, a store wants to make an ad while maximizing efficiency, so you can try to point down the customer profile by looking at the most frequent characteristics of it’s customer base, the mode! As it’s robust to outliers, even if there’s some really highly-different little groups in your sample, you will get a reliable central tendency measure.
Answer:
Mean, median, and mode are measures of "central tendency." They give us an overall indication of what a population looks like.
It also helps to know values of range, standard deviation, variance, etc. Those tell us how "spread out" the values are.
If we consider any diverse group of observations, we might prefer the median to the mean. For example,
With 10,000 people, the mean salary might be $45,000, but the range is $20,000 to $3,000,000 with a mean of $100,000.
In that situation, "outliers" have drastically affected the mean. The few people that earn a lot of money have distorted the overall average (mean). It is better to get the "half-way point" (median). Even the mode (the "most frequent") does not necessarily represent the population, since it could be $25,000, for example.
Some more examples:
grades on a test
height of students (some of whom are on basketball team)
age of employees in a company
... (you can think of a lot more -- diverse is the key).