What is in an average? Is it the most common value? The sum of all values divided by the the number of values? It is just the middle most value?
It is all of these.
The trick is which average you use in which context.
There are three averages i…
What is in an average? Is it the most common value? The sum of all values divided by the the number of values? It is just the middle most value?
It is all of these.
The trick is which average you use in which context.
There are three averages in common use:
Mean
Median
Mode
The mean is the average of all values. It the sum of all numbers divided by the number of values. A useful option when you are comparing groups, have large data sets and more.
The median is the most middle number in a dataset. That is if you listed them all in a hierarchy and split them in half the value on this line would be the median. Good if you have lot of fairly wide spread and data for frequency.
The mode is the most common value. That is the value you see most frequently. Think of the price of a common good and if there is much difference between prices. That similar price is what more than less the mode.
The use of average sis important for this reason. Each is different and therefore using the wrong average in the wrong way can cause all kinds of misunderstandings.
That is because there can be a substantial and significant difference between the average depending on if it was the mean, mode or median.
In fact this difference can be a very useful tool. It tells you a lot about the skew of data. Skew being if it more biased to one side or another of the data.
For example is a class full of tall or short people. It will be more or less positively or negatively skewed.
Generally, if the distribution of data is skewed to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is skewed to the right, the mode is often less than the median, which is less than the mean.
That also means if the mean is misconstrued it can alter the meaning of the data.
