Finding the mean, median, mode, midrange, and outliers of a data set

Intro

Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to find the mean, median, mode, midrange, and outliers of a dataset. Here's our problem statement: Find the mean, median, mode and midrange for the data, and then answer the given question. Listed below are the amounts in dollars it costs for marriage proposal packages at different sports venues. Are there any outliers?

Part A

OK, Part A asks us to find the mean. The easiest way to do that is to dump the data into StatCrunch. Then you use StatCrunch to calculate the mean for us, so I'm going to do that here. OK, my data is now here in StatCrunch. I'm going to resize this window so we can see a little bit better everything that's going on.

OK, now I'm ready to calculate the mean. And to do that, I come up to Stat --> Summary Stats (because I'm looking for a summary statistic; the mean is an example of a summary statistic) --> Columns (because my data is listed there in a column). First, I tell StatCrunch where to find the data, so I select the column with the data. And then notice how we've got some statistics here that are already preselected by default. I don't need all of them. All I want is the mean value, so I'm just going to select the mean, hit Compute!, and there's my mean value. Good job!

Part B

Now Part B asks us to find the median. I could go through those menu options again in StatCrunch, or I could just come up here to the Options button and then press Edit. It takes me right back to the options window where I was previously, and I just switch from the mean down to the median.

Now if I'm smart. I'm going to look here and look ahead and see I'm going to have to calculate the mode. I don't have to calculate the mid range, so let's go ahead and stick the mode in here as well so we don't have to go back and recalculate this. The mode is actually towards the bottom of the list. So to select more than one, I'm going to have to press the Ctrl key and then select Mode. If I hit the Shift key, that's going to select everything in between the median and the mode. And I just want these two statistics to come out.

Notice the order in which they appear here is going to be the same order in which they appear in the results window. So when I hit Compute!, you see here they are in the same order. The mean was first and then the mode. So now I can just stick my answer here in the answer field. Well done!

Part C

Now Part C asks us to find the mode, which we can just come over here to the window. And we don't have to recalculate that; we've already calculated it. Fantastic!

Part D

Find the mid range. StatCrunch actually has no set function for the mid range. I don't know why they don't have it. I mean, it's easy enough to calculate it and code it in, but they just haven't done it. So what we have to do is go about it in a roundabout way.

So I'm going to go back to my options window in StatCrunch. And I'm going to come up here, and I'm going to select two different statistics. The first statistic I'm going to select is the range, and the next I'm going to select as the min. I also select the max so I can demonstrate a second way to calculate the midrange. So now I'm going to hit Compute!

So the midrange is the value that's in the middle of the range between the minimum and the maximum value. So there's different ways to get this out, but you're going to need at least two of these numbers here. And then I'm going to come down here and get my calculator out because we're going to need it. For me, the easiest way to calculate the midrange is just take half the range and then add it to the min. So I can go 2461, which is my range, divided by two. Then I'm going to add that to the minimum value, which here is 39. So I get 1269.5.

I can get the same number if I take half the range and then subtract it from the max value. So again, taking half the range, now I'm going to subtract that from the max value. And see? I get the same number. A third way to calculate it is to just average the min and max values out. So if I want to, I could take 39 plus 2,500, then average that out, and I get 1269.5; it's the same number. Okay, so whichever of these ways is you find easiest for you, that's the way you should go about calculating it. And then just do the same thing every time you're asked to find the midrange. Good job!

Part E

Now Part E asks us to identify any outliers in the dataset. Well, you could look at the data, and you can get a feel that there's going to be a couple of outliers at least here at the end because these numbers here in the triple digits are, you know, so far away from the rest of the dataset. But this 39 here -- it looks like it might be an outlier as well.

The best way to determine outliers from the dataset is to make a graphical representation. And a simple one where you've got a dataset here where you've only got one variable, it should just use a box plot. So if I come back here to StatCrunch and go up to Graph --> Box Plot, select the column with my data, and I want to draw the box horizontally, because then that way it represents more of a number line there on the axis. And it's easier for me to figure out what's going on. I press Compute!, and here's my box plot.

And it looks like that 39 value is not an outlier. But these other two data points that you see represented with the dots are outliers. So 1500 and 2500 are outliers. So I'm going to come back here and select the answer that best says that. Excellent!

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