Standard deviation Simply Explained
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- Опубликовано: 2 окт 2024
- 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)
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Hello Craig, for a 78 year old like me, these are an excellent refresher, (How did i pass my National Certificates , early 1960s ? 😊) ill be able to help the great grandaughters now
with greater confidence ✨️ 🙌
Thank you for taking the time to write this comment. I really appreciate it. Craig
Saying that brings back incredible memories of my great grandfather. He helped me so much with different things. He even took me to school and collected me. I would sit with him for hours in his quiet "living room" and need nothing else. He taught me so much about life, and I think about him every single day that goes by. One the most loved and amazing man that ever lived for me. What you are doing for your great gandaughter will stay deep within her heart for the whole of her life. Keep up the amazing work, thank you again for letting me know. Sorry, i just had to tell you this. Thanks again. Craig
Thank you! Was able to move forward after this video.
Best explanation out there 👍
Thank you. Thumb's upped it. Just curious, how is this so useful, couldn't someone just kind of look at those numbers and see they are more spread out? Thank you!
I knew everything in the video. I want to know what the number (7.07) means in the data if we are not comparing. No value was off by 7.07.
The voice continually says "square" when calculating each action. When calculating the average of the results "square root" is almost inaudible. It took a while to figure this part out. There is no clear explanation about converting negatives to positives. The mechanics are shown, but no explanation as to why.
Thank you so much for such a clear explanation
So clear! So awesome! Other videos left me confused! Now I get it! Thanks so much!
Hi Craig that is a very succinct and clear explanation. Thank you for your effort. When attending a chocka full Uni class where you just have to keep up with the pace- regardless, something is bound not to gel at the time. It’s great to have a simple explanation to do in your own time. Taking it to basic level as compared to a person with a phd , who for them this is probably rather basic… their ability just to keep it straight forward can sometimes not transpose… and you can get stumped and stuck. Your report card shows you have good potential 😊
Thank you for explaining why they get squared! Best video on this topic
You explained it very well
Very cool use of ². Would it not be acceptable to express the individual calculation expressed as (m-'a'=d² vs (m-'c'²=d)?
Very good explanation!! thanks a lot, more video please..
thank you!!
thanks i get answer
Still did not understand it. Like I know how to do the steps and what it says but the answer does not really show any connection to the given data. For example, all the scores in Class A have a difference of 5 but the standard deviation is 7.07. 🤔
Higher SD means the spread of the data is wider, for Class B as you can see there is student who scores 100 and also there is another student who score 40.
I have been looking for this simply clear explanation thank you very much
Amazing video! helped me a lot!
I get it now. Thank you! this video is clear and straight forward.
It is a good idea to add to it what is meant by a small and large SD compared to the mean. I understand that an SD less than 10-15% of the mean is often considered small, while greater than 25-30% of the mean is considered large. A small SD compared to the mean indicates the data tends to cluster around the mean (measure of central tendency), while a large SD compared to the mean means the data is more dispersed away from the mean.
That was very clear, and its 58 years since was last in a school , Thanks 😊
I had already learned this in a class last year but I needed a refresher badly and this did the trick. The explanations for each step were very clear 👍
very clear thanks for this explanation
Excellent explanation. Well done
cool . like your delivery 😁
Very clear explanation. What is the value of knowing the deviation in everyday life?
Hi. Thank you for your positive feedback. I really appreciate it.
As I mentioned in the video, think of standard deviation as a tool that helps you understand how much things vary from what's usual or average. Here's how it can help in everyday life.
Budgeting: Let's say you're tracking your monthly expenses. Knowing the standard deviation of your spending can tell you how much your expenses tend to vary from the average. This helps you plan better and set aside a cushion for unexpected costs.
Weather: When you check the weather forecast, they often mention the temperature's average and the expected range. The standard deviation helps you understand how much the temperature might go up or down, so you know if you need that extra layer or an umbrella.
Cooking: If you're trying out new recipes, knowing the standard deviation of cooking times can give you a range for when the food might be ready. This way, you're less likely to overcook or undercook.
Travel Time: When estimating how long a trip will take, knowing the standard deviation of travel times can help you plan for delays. This is especially handy when you need to catch a flight or make an important appointment.
Fitness Progress: If you're tracking your workouts, the standard deviation of your performance helps you see how consistent you are. It's encouraging to know if you're getting better and how much your results vary.
Product Reviews: When you're shopping online and checking product reviews, the standard deviation of ratings tells you how much people's opinions differ. This helps you gauge whether most people find the product satisfactory or if there's a lot of disagreement.
Exam Scores: In school, knowing the standard deviation of exam scores helps you understand how much the class results vary. It gives you an idea of how tough or easy the exam was for everyone.
In a nutshell, standard deviation helps you make more informed decisions by giving you a sense of how things typically behave and how much they might deviate from what's expected. It's like having a better understanding of the "wiggle room" in different situations, so you can plan and adapt accordingly.
I hope this helps a little, and have a great day
Craig
Thank you for your detailed explanation. It was really helpful. Good luck on your channel. I hope it grows quickly 👍
-10^2=-100
Use parentheses