Article by: Tiago Hands, https://www.instagram.com/tiago_hands
In this article I'll be providing the definitions of the four main concepts in basic statistics, which are the range, mode, median and mean.
Whether you're studying GCSE or A Level mathematics, these concepts are going to be foundational in your learning. The range, mode, median and mean are also used in various job roles such as accounting, investment banking and sports analysis. In fact, it's hard for ordinary people to get by in life without using averages.
So, below are the four main concepts you need to know before producing any kind of meaningful statistics:
The Range
The range is simply the difference between the highest and lowest value in a data set. Let's say we have the values:
2, 3, 7, 14, 21, 29, 34, 61, 98, 105
What would the range be? Well, the lowest value is 2 and the highest value is 105. This means that the range would have to be 105-2=103.
Formula: Highest Value - Lowest Value = Range
The Mode
The mode is the value that occurs most often in a data set. If we have the values:
2, 3, 9, 5, 6, 7, 7, 4, 15, 21, 7, 7, 8, 7, 3, 1
We'd have to say that 7 is the mode. That is because it appears the most. If however we have the values:
2, 3, 2, 7, 7, 9, 9, 2, 8, 9, 10, 11, 12
We'd have to call our data set bimodal. This is because the values 2 and 9 appear the most often and each 3 times.
If all the numbers in a data set appear as often as each other, there is no mode.
The Median
If you put a data set in order and obtain the middle value, what you'll get is the median. So for instance, if we put this data set in order:
1, 5, 6, 2, 3, 7, 9, 10, 12, 15, 14, 13, 18, 21, 19
--> 1, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 15, 18, 19, 21
We'd have to call the median 10, as it's the middle value. It sits in position 8 out of 15 ordered numbers.
There is a formulaic way to get the median value of an ordered data set. Get the number of observations that exist (n), in this case 15, then divide by 2. If n/2 is not whole, then round your result up and get the corresponding value. With the data set we're dealing with n/2 would yield the result 7.5. So we'd say that the median value is the 8th term. Once again the median would end up being 10 based on the set of values above.
So, what would happen if n/2 is whole?
Say we have the ordered data set:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
There are 10 observations so n/2 would be equal to 5. Since 5 is whole, we'd have to get the middle value between the 5th and 6th term. The middle value between 5 and 6 is 5.5, therefore in this case the median would be 5.5. This is the same as (5+6)/2.
Let's try out another data set:
1, 4, 5, 7, 9, 12, 13, 17
Here there are 8 observations - in order. 8/2 is equal to 4. Since 4 is whole, we have to find the mid-point between the 4th and 5th value. That would be (7+9)/2=8. The median in this case would be 8.
The Mean
The mean is equal to the sum of observations (Σ) divided by the total number of observations (n). With the data set below (x), what would the mean be?
x = {1, 2, 5, 7, 9, 12, 15, 18, 35, 36, 49}
n = 11
Well, the sum of observations (Σx) is:
Σx = 1 + 2 + 5 + 7 + 9 + 12 + 15 + 18 + 35 + 36 + 49 = 189
And there are 11 observations (n=11), so:
(Σx)/n = 189/11 = 17.18 (to 2 decimal places)
Therefore in this case, the mean would be 17.18 to 2 decimal places.
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I hope this article will be of massive use to you. Since I'm always dealing with data, using the range, mode, median and mean is just natural to me. I've been quite good at mathematics my entire life and I really can't remember a day when I didn't use at least one type of average.
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Good one