The mean is the average of a set of numbers, temperature readings say, add them up, divide by the number of temperatures.
The mean is used to compare samples and populations using statistical tests, difference between means etc.
e.g.
5.4°C
3.5°C
2.4°C
4.7°C
The total is 16°C, divide that by the number of temperatures and the mean or average is 4°C.
Now let us change the 5.4°C to 9.4°C
9.4
3.5
2.4
4.7
Total is 20, divide by 4, average or mean temperature is now 5, so large outliers really move the mean towards the outliers. For this reason to compare two sets of figures the median is used. Let us look at another set of temperatures:
10.2
11.3
9.5
8.7
10.3
All °C of course. What we do first is rearrange the numbers:
8.7
9.5
10.2
10.3
11.3
The median is that value that has half of the set of numbers (a sample) less than the median value and half the set of numbers greater than that value. We see that 10.2 is the median, 2 readings below it and 2 readings above it. You could change the 11.3 for 111.3 and the median would still be 10.2.
Now the mode is the value with the largest number of readings. In our little set of 5 temperatures if we change the 10.3 to 10.2 we get
8.7
9.5
10.2
10.2
11.3
10.2 is obviously the mode.
The mean, median and mode are measures of central tendency, where the centre of the distribution of the values in our samples is. Looking at the series, looks like Greenland summer temperatures
Next we want to know how tightly the values are distributed around the mean, median or mode.
The range is simply the difference between the smallest and largest value, 11.3 - 8.7 = 2.6. Not the most useful measure
Variance, standard deviation is measured by squaring the difference between each value and the mean. Going back to our original sample:
5.4°C
3.5°C
2.4°C
4.7°C
Mean is 4°C so (4-5.4)
2
and we go through to 3.5, 2.4 etc.
Because values are either side of the mean we need to square each individual variance, if we just added up the differences from the mean we end up with zero (where the values are equally distributed around the mean.) Won’t give the formula, won’t have much meaning to you. But variance just tells you how spread out the distribution of your sample is. Standard deviation is used in statistical tests such as difference of means.
Kurtosis—a measure of how peaky the distribution is, and skew is how much of the distribution is at one end of the distribution. Don’t worry about it.
The mean and standard deviation describes the distribution, the set of temperature readings and allows tests to be made.
Hope it helps.
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