In this video we discuss the measures of central tendency, as we find and compare the mean, the median and the mode, in an example of drafting a running back for your fantasy team. We also cover how the shape or skew of a distribution affects each of them. Transcript/notes
Measures of central tendency and comparing the mean mode and median.
Lets look at the measures of central tendency, the mean, median and mode, and also compare them.
So, lets say you are looking to draft a running back for your fantasy football league, and here is the game logs for rushing yards, in this case our data set, for a player you are thinking about drafting, over a the previous 16 game season.
We are going to quickly calculate the mean median and mode and compare them for rushing yards per game for this player.
To calculate the mean or average, we add up all the values and divide by the total number of values. Adding them up we get 1307, and there are 16 total values. So, 1307 divided by 16 equals 81.7, which is the mean rushing yards per game.
Now for the median, which is the middle value, or between the middle values. Since we have 16 total values, and even number of values, it will be between the middle values. We will arrange the values in ascending or increasing order, draw a line here in the middle, where we have 8 values lower, and 8 values higher. And add these 2 middle values together and divide that total by 2, which gives us 74.5, which is our median.
Now for the mode, which is the value that occurs the most in the data set. Looking through, we see that 43 is the most occurring value, twice, so our mode is 43.
So, 81.7 is the mean, 74.5 is the median, and 43 is our mode. In comparing the 3 of these, we see the mode is extremely high, and the median and mean are kind of close. So, the mode is probably not the best tool to use in evaluating this running back.
All 3 of these tools can be influenced by the skew of the data. For instance, a symmetrical distribution, as you see in this graph, has some high and some low values, and some values in between. So, the mean, median and mode will lie near the middle.
In a positively skewed distribution, the higher values in the data set will pull the mean upwards, the median will be less than the mean, and more towards the center of the graph, and the mode will be less than the median, more towards the peak of the graph.
And in a negatively skewed distribution, the lower values will pull the mean downwards, the median will again be near the center of the graph, higher than the mean, and the mode will be the highest of the 3, near the peak of the graph.
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