Standard deviation? In simple words

 Standard deviation is a measure of how spread out a set of numbers is. Imagine you have a bunch of numbers, and you want to know how far they are from the average (or mean) of all the numbers. Standard deviation is a way to measure this.

Here's an example: let's say you have the following set of numbers: 1, 2, 3, 4, 5. The mean of this set is 3 (you get this by adding all the numbers up and dividing by 5). Now let's say you want to know how far each number is from the mean. To find the standard deviation, you would do the following:

How to find it:

For each number, subtract the mean from the number. This will give you the difference between the number and the mean. For example, for the number 1, the difference would be 1 - 3 = -2.

Square each of the differences you calculated in step 1. This will give you the squared difference for each number. For example, the squared difference for the number 1 would be (-2)^2 = 4.

Add up all the squared differences. This will give you the sum of the squared differences.

Divide the sum of the squared differences by the total number of numbers in the set. This will give you the average squared difference.

Take the square root of the average squared difference. This will give you the standard deviation.

What it means:

In this example, the standard deviation would be 1.58. This means that the numbers in the set are, on average, 1.58 away from the mean. A smaller standard deviation means that the numbers are closer to the mean, while a larger standard deviation means that the numbers are more spread out.

Example: (this is from an exercise in the lesson)

Which of the below data sets has the lowest standard deviation? You do not need to calculate the exact standard deviations to answer this question.

The data set with the lowest standard deviation is 100, 100, 100, 100, 100, 100, 101. Standard deviation is a measure of how much the values in a data set vary from the mean. In this case, all of the values are very close to each other and the mean, so the standard deviation is very low. In contrast, the other data sets have a wider range of values and larger deviations from the mean, so their standard deviations are higher.

100, 100, 100, 100, 100, 100, 101

0, 25, 50, 100, 125, 150, 1000

0,1,3,3,3,5,6

0,1,2,3,4,5,6