The Arithmetic MEAN Measures of Central Tendency 5 6

foreign there are three measures of central tendency the mean the median and the mode now we're going to talk about the mean the mean is the score located at the mathematical center of distribution the mean is the most commonly used measure of central tendency when we have interval or ratio level data what we have also called scale level data and the mean is most commonly meant when someone talks about an average it is possible to call the mean the median and the mode all the average but we want to be careful about how we use that word average it implies the mean you want to be aware if someone is trying to mislead us with statistics by calling let's say the median an average it's important that we distinguish if we use mean and call it the average that's what's expected but if you use the mode or the median you can call it an average just be sure that you specify that you're using the median or the mode later when we learn about the normal distribution we will discover that the mean the median and the mode are approximately equal in normal distribution we will also use comparison of the median and the mean as we learn about skewness when should choose mean as my measure of central tendency the mean is an excellent planning value it is quite possible that the mean will not be score that actually exists in the data set such as the average American family has 2.5 children but that value can be useful when planning for the future for example let's say that Springfield is slated to grow by 1 000 families in the next five years this could help us determine how many additional classroom seats we're going to need in our Public School if the average family has 2.5 children then over the next five years we should expect an enrollment increase of approximately 2 500 children that's what mean by the mean being useful as measure for planning the mean is also useful Choice when we want stable measure one thing to know about the mean however is that it is relatively stable measure meaning that although it is susceptible to outliers it takes either very extreme outliers or lot of outliers in order to strongly influence the mean for the most part although outliers do affect the mean outliers are not going to dramatically change the mean unless there are lot of them or they exert lot of Leverage in our data that's what mean by relatively stable but in order to use the mean the data must be at the scale level we can't use mean with nominal or ordinal data and think about why that would be nominal data the numbers don't mean anything they can't be added or subtracted there's no math that we can do with the jersey numbers ordinal data the difference between first second third fourth place can't be meaningfully combined so that we say the the average was finishing 2.5 place so we will only use mean with interval or ratio also known as scale level data and in addition we want to assure that our data are not excessively skewed meaning that they have extreme outliers on only one end of the distribution because that truly could affect the usefulness of our mean now told you about the mathematical average of the mean however there are other measures of the mean that we need to learn about