The number of short-term parking spaces at 15 airports is shown. Find the mean, median, mode, an

The number of short-term parking spaces at 15 airports is...

Key Concepts

Midrange

The midrange is a measure of central tendency calculated as the average of the smallest and largest values in the dataset. It gives a quick sense of the data’s spread and central value, although it can be heavily influenced by outliers.

Mode

The mode is the value that appears most frequently in a dataset. A set of data may have one mode, more than one mode if there are ties, or no mode if all values appear with equal frequency. It provides insight into the most common or popular value within the data.

Mean

The mean is the arithmetic average of a set of numbers, calculated by summing all the numbers and then dividing by the count of numbers. It is used to provide a single value that represents the central tendency of the entire dataset.

Median

The median is the middle value of a dataset when the numbers are arranged in order. For an odd number of observations, it is the central number; for an even number, it is the average of the two central numbers. The median is particularly useful in mitigating the effect of outliers on the overall central tendency.

Transcript

00:01 In this problem we've been given 15 pieces of data and our data set along the left side here and we're being asked to find the four measures of central tendency the mean the mid -range the median and the mode i've taken one step ahead of time that you should also take and that's to put all of my pieces of data into ascending order you can see that i have the lowest number this 203 up at the top and then that goes all the way down to my highest value which is 9 ,822 at the bottom doing this is really important any time you have a data set that has more than four or five elements in it, because it's going to make it much easier for us to find three of our four measures of central tendency.

00:39 Also, you're going to need a calculator of some kind.

00:41 It can be scientific, it can be desmos, just something that can handle kind of mundane arithmetic, like adding some of these really large numbers together.

00:49 So let's go ahead and get started.

00:51 First we're going to need to find the mean.

00:52 The mean is the average of all of our numbers, and the way that we do this is that we find the sum, of the entire list by adding them all together, and divide by the number of elements in the list that we have.

01:03 Since we already know that there are 15 elements, there's going to be a 15 on the bottom here.

01:08 What we don't have yet until we punch it into our calculators is the sum.

01:11 So right now, go ahead and take that step.

01:13 Add these up in your calculator and get the sum.

01:16 What you should end up with is 47 ,619.

01:21 That's the sum, and we know that underneath it we have the number of terms, which is 15.

01:25 So now if we divide these two values, we will come up with our mean for which we get the value 3 ,174 .6.

01:37 There's our mean, and probably the hardest of all these problems in the bag already.

01:41 Next up is our mid -range, which is a lot like the mean, but instead of finding the average of all the numbers, we're only finding the average of the top and the bottom values, the lowest, and the highest.

01:52 If you feel like you need a formula for this, i would probably call this low plus, high and then unlike our mean where we had 15 numbers here we're only going to be adding two so that's what we'll divide by in order to get our average so let's go ahead and do this plug in our numbers our lowest number is 203 and our highest number is 98 22 don't forget that we're going to divide this by two afterward and we'll take an intermediate step and actually put these together so this makes 10 ,000 25 over 2 and then finally we can divide this in our calculator to get a mid -range of 512 .5.

02:37 Looks good.

02:38 Now we're going to go to our median next and the median is kind of there are a couple of ways that you can do it.

02:44 We'll start by brute forcing it.

02:46 What the median is asking for is it's asking for the value exactly halfway through your list.

02:51 This is the one that benefits the most from putting everything in order.

02:56 So the what i call this, i'm going to say that this is the middle, the middle number in your sorted list of data.

03:07 Okay, root forcing this is about just taking the top and the bottom values you have and chopping them both off, and we'll keep doing that until hopefully we only have one value left...

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