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Earth Science 102: Weather and Climate13 chapters | 127 lessons

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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.

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.

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.

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.

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.

Now, plug in 15 for N. Remember, deal with what's inside the parentheses first, so 15 plus 1 is 16. And then 16 times 1/4 is 4. So our first quartile is the 4th number in our list. Start counting from left to right until you get to the 4th number. One, two, three, four.

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

Ok, it looks like 4.7 is our first quartile number.

The first quartile represents the 25th percentile. Meaning, 25% of the temperatures are below or equal to 4.7 degrees F.

The second quartile is actually the median (and remember how we calculated that, right?). If, in the future, you don't want to cross off numbers, there's a formula for you:

1/2 (N+1)

So, 1/2 (15+1) = 8. So, the 8th number is the median.

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

Which is 6.5. Yep, that was the median we calculated in the previous segment. So look at that, you have two ways to calculate the median - otherwise known as the second quartile. This is the 50th percentile, meaning 50% of the temperatures are below or equal to 6.5.

And the third quartile is calculated using the formula:

3/4 (N+1)

So, 3/4 (15+1) = 12. Go ahead and count 12 numbers from left to right.

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

Ok, it looks like 8.6.

This third quartile, or 75th percentile, means 75% of the temperatures are below or equal to 8.6.

So, why in the world would you take the time to calculate the quartiles? Well, let's say you are having a particularly cold winter in Fairbanks, Alaska. You can take a look at the quartiles from the previous years to see how this year's temperatures compare. Are the temperatures in the 25th percentile, or first quartile? Or are they in the 75th percentile, or third quartile? This helps you see if you are truly having a cold winter or if it actually is just average.

The **range** is the difference between the largest and smallest value of numbers. In our case, the range would be the difference between our smallest temperature, 3.4, and our largest, 10.1. So:

10.1 - 3.4 = 6.7

Figuring out a range is great because scientists can see how much the temperature fluctuates over a period of time. For example, the high temperature varied by 6.7 degrees F in the first 15 days of February. It would be useful to compare this fluctuation from year to year.

When someone says 'Temperatures have really risen over the last few years,' you can ask them if they are talking about the average temperatures like mean or median, the quartile temperatures, or the range. Remember, the **mean** can be calculated by adding up all of the temperatures and dividing by the total number of temperatures. The **median** can be calculated several ways. The first is to place the numbers in order from smallest to largest and then cross off one number from each side until you reach the middle. If you have an even number of temperatures, you need to complete one additional step: finding the mean of the last two numbers in the middle. You can also use the formula 1/2 (N+1).

In order to group the numbers, you can calculate **quartiles**, which groups values into the first quartile, the second quartile, and the third quartile. There are formulas you can use here, too:

1/4 (N+1)

1/2 (N+1)

3/4 (N+1).

Quartiles allow you to see which values are in the 25th, 50th, and 75th percentiles.

Next, it's valuable to look at the **range**, which can be calculated by taking the largest value minus the smallest value.

Wow! That was a lot of math! But, it is important, from a scientific standpoint, to examine temperature changes over a period of time to ensure the trend is an overall warming or cooling and not just a warm or cool year. By learning how to find the mean, median, quartile, and range you can do just that! These calculations help you determine if you are witnessing **climate variation**, meaning the fluctuation of climate above or below the average, or if you just had an exceptionally hot couple of days.

After you have finished with this lesson, you should be able to:

- Recall how to calculate the mean, median, quartile, and range
- Explain how these calculations help scientists study climate variation and temperature

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Earth Science 102: Weather and Climate13 chapters | 127 lessons

- Go to Climate

- Temperature Units: Converting Between Kelvins and Celsius 5:39
- Factors that Influence Earth's Temperature 7:48
- Daily & Annual Temperature Patterns 9:08
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- Temperature Ranges by Seasons and Climates 7:55
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