# Mean, Median, Quartile, Range & Climate Variation of Temperature

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• 0:01 Climate Variation
• 1:32 Mean
• 3:33 Median
• 5:39 Quartile
• 8:22 Range
• 8:56 Lesson Summary

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Lesson Transcript
Instructor: Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

Believe it or not, there is a lot of math involved in temperature. This lesson will teach you how to calculate the mean, median, quartile, and range and explain how these calculations help you understand climate variation.

## Climate Variation

So you've probably never thought much about doing math when you look at your thermometer outside, right? You take a look, see it's 60 degrees F, put on a light jacket, and head out. But, there is actually quite a bit of math that can be involved in temperature! By completing a few calculations, scientists can better understand climate variation, or how the climate fluctuates above or below the average over a period of time.

These calculations are relatively simple. In fact, we're going to do some in this lesson! We will use data to calculate average temperatures, or the mean, and median. Scientists use these averages to see how temperatures change over time. Then we will break the numbers down into quartiles, otherwise known as percentiles. And, finally, we will look at the range in order to see how the temperatures vary over a period of time.

All of this data helps scientists better understand climate change and global warming. For example, maybe you are having an exceptionally hot winter. Scientists can look at the mean and median of past winters to determine if your winter is an anomaly or part of a warming trend. Scientists can also look at quartiles to see where your winter falls. Is your winter in the 75th percentile - or warmer than 75% of the other winters on record? Or is it just slightly warmer? Finally, by looking at the range, scientists can determine if your winter has a lot of fluctuation or consistently warm days.

## Mean

Let's start by discussing the mean, and no, I'm not going to start yelling at you. This is a different type of 'mean.' In math, the mean is the average. You can find daily means, weekly means, monthly means, and even yearly means. As mentioned earlier, the mean is helpful in looking at climate, or how the mean temperatures vary from year to year. Let's use Fairbanks, Alaska, to practice calculating the mean. So, pause the video and grab some scratch paper, a pencil, and a calculator.

Take a look at the table below. It shows the daily high temperatures for the first half of February in Fairbanks, Alaska. You'll notice we are using degrees Fahrenheit, but scientists also use Celsius or Kelvin. We're going to calculate the mean temperature for the first 15 days in February.

February date High temperature (Degrees F)
1 3.4
2 3.8
3 4.2
4 4.7
5 5.1
6 5.6
7 6
8 6.5
9 7
10 7.5
11 8
12 8.6
13 9.1
14 9.6
15 10.1

To do this we just need to add up all of the temperatures and divide by the total number of temperatures (which is 15).

Let's get started. You can pause the video and take a moment to add up the temperatures.

Okay, it looks like all of those temperatures added together is 99.2. Is that what you got? Now, to find the mean, you take 99.2 divided by however many temperatures there were, which was 15. So...

99.2/15 = 6.6

So, our mean is 6.6 degrees F.

So remember, to find the mean you add up all of the values and divide by however many values are present. In our case, we added up the first 15 high temperatures for February in Fairbanks, Alaska, and then divided by 15.

When you are studying climate, it is useful to look at mean temperatures over a long period of time. This allows scientists to see if there is an overall trend in temperature change or if one or two years were just an anomaly.

## Median

The mean isn't the only tool we can use to look at averages. We can also look at the median, which is the middle temperature. To understand what that means, let's look at that table again:

February date High temperature (Degrees F)
1 3.4
2 3.8
3 4.2
4 4.7
5 5.1
6 5.6
7 6
8 6.5
9 7
10 7.5
11 8
12 8.6
13 9.1
14 9.6
15 10.1

Now, to find the median, arrange the temperatures from coldest to warmest and start crossing off one number on each end.

3.4, 3.8, 4.2, 4.7, 5.1, 5.6, 6, 6.5, 7, 7.5, 8, 8.6, 9.1, 9.6, 10.1

So I will cross off 3.4 and then 10.1. Next, I will cross off 3.8 and 9.6, then 4.2 and 9.1, and then 4.7 and 8.6, and so on and so forth. When you have one number left, that is your median. Why don't you pause the video, keep crossing, and then check back with me?

If I keep crossing them off, I am left with 6.5. So our median is 6.5 degrees F. Remember, a median is the 'middle' value, which means that half of the temperatures are greater than or equal to the median and half are less than or equal to the median.

But what happens if your list of numbers is even and not odd like our set of 15? Let's pretend we had a list of six numbers. You would start by putting them in order from smallest to largest, just like before.

1, 3, 4, 5, 7, 10

Next you would start crossing them off like before. So I'd cross off 1, then 10, then 3, then 7. But you'll notice, since there are six numbers, there is no middle, and I have both 4 and 5 left. So, in this case, you find the mean of these two, and this gives you the median. Remember, to find the mean, you add 4 plus 5 and get 9 and then divide by 2, which gives you 4.5.

The median is good because it can give you a general idea of the average without getting skewed by outliers. For example, let's pretend you had the following data set for temperatures:

Day Temperature (Degrees F)
1 0
2 40
3 40

The mean would be 26.7 degrees F, and the median would be 40. So you can see how that outlier of 0 degrees F really impacts the mean but not the median.

## Quartile

Now, we can take our temperature list and find the quartiles for the first half of February. Quartiles are the values that divide a set of numbers into groups: the first quartile, the second quartile, and the third quartile. Let's go over how to calculate the quartiles.

Start by putting our number list in order from smallest to largest.

3.4, 3.8, 4.2, 4.7, 5.1, 5.6, 6, 6.5, 7, 7.5, 8, 8.6, 9.1, 9.6, 10.1

To figure out the first quartile, you can use the formula:

1/4 (N+1) where N = the number of temperatures, so 15.

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