Here I Simply Explain Standard Deviation.
Consider a collection of numbers, such as the test results of your classmates. Some results may be very near to the mean while others may be very far from it. You can determine how far those scores deviate from the mean by using the standard deviation.
How it functions
Say you received the following test results: 70, 75, 80, 85, and 90. 80 is the average (mean). Let's check how far each score deviates from the mean now:
(80 - 70) 10 points less than the average is 70.
(80 - 75) 5 points less than the average is 75.
80 is around typical (80 minus 80 equals 0).
(85 - 80) 85 is 5 points more than the average.
90 (90 - 80) is 10 points higher than the average.
Let's now calculate the distance between those differences. We multiply the following squared discrepancies:
10^2 + 5^2 + 0^2 + 5^2 + 10^2 = 100 + 25 + 0 + 25 + 100 = 250
The square root is then obtained by dividing the total by the number of scores (five):
√(250 / 5) = √50 ≈ 7.07
The standard deviation is approximately 7.07, as shown. It informs you that the scores are typically 7.07 points outside of the norm.
In other words, standard deviation makes it clearer how much a group's scores deviate from the mean. Small standard deviation indicates that most scores are within a few points of the mean. Scores deviate further from the average if it is large. It functions as a means to gauge how uniform or dispersed the numbers are.
Have a great day
Craig (from Kirkman's Academy)
