Statistics Tutorials: Mean, median and mode

Key Takeaways

this lesson will introduce you to the three measures of central tendency don't be scared by the terminology we are talking about mean median and mode even if you are familiar with these terms please stick around as we will explore their upsides and shortfalls ready let's go the first measure we will study is the mean also known as the simple average it is denoted by the Greek letter mu for a population and x-bar for a sample these notions will come in handy in the next section we can find the mean of a data set by adding up all of its components and then dividing them by the number of components contained in the data set the mean is the most common measure of central tendency but it has a huge downside it is easily affected by outliers let's compare these two datasets these are the prices of Pizza at 11 different locations in New York City and 10 different locations in LA let's calculate the means of the two data sets using the formula for the mean in NYC we get 11 dollars whereas for LA just 5.5 on average Pizza New York can't be twice as expensive as in LA right correct the problem is that in our sample we have included one posh place in New York where they charge $66 for pizza and this doubled the mean what we should take away from this example is that the mean is not enough to make definite conclusions so how can we protect ourselves from this issue you guessed it we can calculate the second measure the median the median is basically the middle number in an ordered data set let's see how it works for our example in order to calculate the median we have to order our data set in ascending order the median of the data set is the number at position n plus one divided by two in the ordered list where n is the number of observations therefore the median for NYC is at the six position or $6 much closer to the observed prices than the mean of eleven dollars right what about LA we have just ten observations in LA according to our formula the median is at position five point five in cases like this the median is the simple average of the numbers at positions five and six therefore the median of LA prices is five point five dollars okay we have seen that the median is not affected by extreme prices which is good when we have posh New York restaurants in a Street pizza sample but we still don't get the full picture are the majority of restaurants low cost or average we must introduce another measure the mode the mode is the value that occurs most often it can be used for numerical and categorical data but we will stick to our numerical example after counting the frequencies of each value we find that the mode of New York Pizza prices is three dollars now that's interesting the most common price of pizza in NYC is just three dollars but the mean and median led us to believe it was much more expensive okay let's do the same and find the mode of la Pizza prices hmm each price appears only once how do we find the mode then well we say that there is no mode but can I say that there are ten modes you may ask sure you can but it will be meaningless with ten observations and an experienced statistician would never do that in general you often have multiple modes usually two or three modes are tolerable but more than that would defeat the purpose of finding a mode there is one less question that we haven't answered which measure is best the NYC and LA example shows us that measures of central tendency should be used together rather than independently therefore there is no best but using only one is definitely the worst for more videos like this one please subscribe