Statistics for IGCSE/ O-level students

Statistics for IGCSE/O-level Students

Introduction
Statistics is a very important section of mathematics. However, it can get quite deep, as it is, after all, statistics. However, this statistics course will not be too deep, and this lesson is literally a breeze for those with some exposure to statistics.

Terms
Mean
In this case, we are referring to the arithmetic mean, which is basically the sum of all values in a data sample divided by the number of values.
Example: 1, 2, 3, 4, 5
The sum of all values is 15
The number of values is 5
Hence the mean is: 15/5 = 3

Range
This is the largest value minus the smallest value in a data sample.

Example: 1, 6, 7, 8, 10
The largest value is 10
The smallest value is 1
Hence the range = 10 – 1 = 9

Mode
This is the most common value in a data sample.
Example: 2, 2, 2, 4, 4, 5
Which value appears most often? 2, right, as it appears three times. Therefore, 2 is the mode.

Median
This is the middle value of the data sample.

Basically, after you choose the number, there is an equal number of numbers on the left and right of the data sample. There are two approaches to calculating the median, and they can be classified as:

Even number of data points in the sample.
Odd number of data points in the sample point.
Odd Number
This one is extremely easy.
Let's say you have the data samples 1, 2, 5, 6, 7.
Now, we have 5 numbers. We want to find the middle number, so let's find the middle number:
1 2 5 6 7
Yes, 5 is the middle number, so therefore, it is the median.

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Even Number
This is more tricky, but still quite easy.
Let's look at the data in this sample:
1, 5, 6, 7, 8, 9.
The middle number is more tricky because you don't know whether 6 or 7 should be considered as the middle number. If you pick 6, then there will be an uneven distribution of numbers on the left and right. The same will happen if you picked 7.
So, there is a simple equation you can use:
(N + 1) / 2
Where N is the number of terms in the data sample, which in this case, is 6.
So, plugging in the numbers we get:
(6 + 1) / 2
= 3.5
So, the third and a half term.
Basically, the 3.5 term is in between the 3rd and 4th term, so what we do here is we find the mean of the third and fourth term.
The 3rd term is 6, the 4th term is 7, so the average will be:
(6 + 7) / 2
= 6.5