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Normal Distributions, Standard Deviations, Modality, Skewness and Kurtosis: Understanding concepts
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- Опубликовано: 6 авг 2024
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Normal distributions, Modality, Skewness and Kurtosis: Understanding the concepts
The normal distribution is a theoretical concept of how large samples of ratio or interval level data will look once plotted. Since many variables tend to have approximately normal distributions it is one of the most important concepts in statistics. The normal curve allows for probabilities to be calculated. In addition, many inferential statistics require that data are distributed normally. If your data is not normal be careful what statistical tests you use with it.
In a normal distribution, measures of central tendency including the mean, median and mode all fall at the same midline point. The mean, median and mode are all equal. The calculation of these measures of central tendency are covered in another video.
Normal distributions share several key features. They are unimodal, meaning that there is only one peak in the distribution.
When divided at the mean a normal distribution takes the form of a symmetrical bell-shaped curve.
Standard deviations are used to measure how much variation exists in a distribution. Low standard deviations mean values are close to the mean whereas high standard deviations mean that values are spread out over a large range.
In a normal distribution approximately 34% of scores fall between the mean and 1 standard deviation above the mean. Therefore, based on it's symmetry, approximately 68% of scores fall between 1 standard deviation above and 1 standard deviation below the mean;
approximately 95% of scores fall between 2 standard deviations above and 2 standard deviations below the mean;
approximately 99.7% of scores fall between 3 standard deviations above and below the mean.
Z scores are used to measure how many standard deviations above or below the mean a particular score is. These scores allow for comparison and probability calculations.
Not all samples approximate a normal curve.
To understand more about distributions it is important to understand modality, symmetry and peakedness.
A distribution can have more than one peak. The number of peaks contained in a distribution determines the modality of the distribution. Most distributions are normally distributed and have only one main peak, meaning they are unimodal. However, it is possible to have distributions with two or more peaks. Distributions with two peaks are bimodal. Distributions with more than two peaks are multimodal.
Symmetry and modality are independent concepts. If two halves of a distribution can be superimposed on each other where each half is a mirror image of the other, the distribution is said to be symmetrical.
Sometimes data are not symmetrical. If the peak is off centre one tail of the distribution will be longer than the other, meaning it is skewed.
Skewness is a measure of the symmetry of distributions. Pearson's skewness coefficient provides a non-algebraic, quick estimation of symmetry.
Recall that Normal distributions are symmetrical and bell shaped. In a perfect distribution the skewness coefficient will be equal 0 because the mean equals the median.
Positive skewness means there is a pileup of data to the left leaving the tail pointing to the right side of the distribution. The tail has been pulled in the positive direction. The data is skewed to the right. In this case the Mean is to the right of the median. Interestingly, positive skews are more common than negative ones.
Negative skewness means there is a pileup of data to the right with a long tail on the left side. The tail has been pulled in a negative direction. In this case the Mean is to the left of the median.
To remember the meaning of a positive and negative skew think of pulling on tails. Remember that the tail points towards the direction of the skew. The mean is also pulled in the direction of the long tail of the skew.
Kurtosis is a measure of the shape of the curve. It measures if the bell of the curve is normal, flat, or peaked. Since it's calculation is tedious it is typically done by a computer.
Using Fisher's measure of kurtosis a normal distribution would receive a coefficient of 0 and be called mesokurtic.
If the calculation of excess Kurtosis results in a large positive number the distribution is too peaked to be considered normal. This type of data is called leptokurtic. The curve is taller and skinnier than a normal distribution. The beginning of the word kind of sounds like leapt so think of a skinny guy who leapt high in the air....
![USEFUL OR TRASH? Kurtosis and Skewness [WATCH THIS, BEFORE YOU USE]](http://i.ytimg.com/vi/Nhpe0uSf0Ts/mqdefault.jpg)
As an instructor myself I wanted to commend you on your ability to explain a difficult concept without talking over the listener's head. So many videos get so caught up in the math and details they often forget how important it is sometimes to simply explain what's going on in terms anyone can understand.
Thanks for the video. Lepto means narrow (or thin) in Greek. Platy means wide. Just thought I'd throw that out there in case it's useful to anyone.. thanks again for the video!
These are very clear and simple descriptions for very mud-like processes! Thanks so much. I am going to share with my Ed.D. Ed Leadership cohort. You rock!
As a novice to Statistics your ability to educate by captivating the learner is a tremendous skill set not found in many instructional videos! THANK YOU, and well done!
you basically summed my two hour lecture into a five minutes video whilst also making it very simple to understand. thank you!
Definitely one of the best simplified mini lessons for statistics!
Just what I needed. good clear explanations. good audio, good visuals. Keep up the good work.
Thank you. I have been searching for a good video on distribution curves and this is the best one. It answered all my questions. Much appreciated
professionally simplified, as a step towards heading to the complex understanding. Great!
This one is quite helpful and understands concepts from a visual perspective. Kudos to @Nursekillam
Thank you. Your effort is highly appreciated
It is important to highlight that the Kurtosis they mention in the video is the so-called "excess kurtosis" which has the value of 0 in the case of a Normal Distribution. Kurtosis, on the other hand, is 3.
This is really great. So much information in such short video with such clarity.
This is the best explanation I've found on RUclips. Thank you!
This video is the first on the subject to really help me understand. Thank you for the clear explanation :)
You are welcome :)
Thanks very much NurseKillam. I was struggling to understand the concept of kurtosis. Yours is the best video I've seen!!!! :)
Your videos and explanations are very good. Thanks for putting this up.
Thanks very much from Belize. Short and to the point, but very effective. Never seen so much info presented so clearly in such a short time. Thanks again and great work.
Thanks :) ... It definitely takes some effort to accomplish that.
I love how u explained it so simply! thanks
+Nena Miodrag you are welcome. That was my goal :)
Very informative with all those figures, thank you so much!
Really great video tutorial. It is useful for beginner and expert as well.
It's really helping our students coz it's a very simple and clear explanation, thank you so much.
Great explanation and easy to understand thanks for the visual.
Thank you!! Just started my doctoral program and needed some further assistance!!
Thank you so very very much! You helped me to identify with kurtosis because the reading was too much in my texts.
THANK YOU!! FINALLY SOMEONE EXPLAINED WHAT THE KURTIC'S LOOK LIKE
Thanks soooo much! Great Clarity, in your speech and in your presentation! Excellent!
Thank you!
Awesome presentation. So happy I watched the video. Thanks so much :)
Its Great! Helped me with the basic, but you should make detailed videos. I'd love it!
this video is very helpful for the beginner. thank you so much ma'm.
Precise, to the point and complete.
Thank you for your time. It's a valuable information that it helps me with my class.
+Charles Spurgeon So good to hear
Precise and straight to the point! very heplful..thanks!!
Really simple and perfect expalanation.
Awesome video. Thanks for uploading!
Very simplistic, thank you, anyone could follow specially for a beginner like me.
It was really helpful, easy to learn , Thanks a lot
Simply excellent. Very grateful for clear, concise and well presented video. Thank you for the great channel. 27/8/2018 😊
Wow can I adopt you as the stats teacher character in my life? You explained that articulately! :D
:) thanks
Great explanation! Thank you!
Really excellent explanation! Many thanks 🙏
Nice video. I am just familiarising myself with the concepts so it was nice and conceptually clear, but also with a chance to learn some fancy terminology on the way :)
Very useful presentation! Thank you!
I'm happy you liked it
Thanks
+Josh Uddin yes. I'm a nurse and teacher.
thank you ma'am it was very helpful for me :-)
Thanks for this basic, intuitive explanation :)
You are welcome
Thank you for the video. It was very helpful :-)
Statistics is still beyond confusing but this video helps. No longer dazed and confused, just confused. Thanks for making it.
simple and informative, thank you
Well explained and thank you so much.
Crystal clear explanation...
Thank you. Your videos are helpful.
Very helpful!
will be looking for other videos from you on Statistics~
+Sharon T Thank you. I hope to make more soon. Is there anything you need in particular?
Thanks for the simplified Explanation 🙏
Pls, how do we solve different problems concerning Skewness and Kurtosis?
awesomely clear explanations
Nursekillam I legit love you!! your video is awesome!!
Thanks for the breakdown!!!
Very good video. Thanks for posting it.
. very nice .. i was absent during our class discussion regarding this topic . and it's our exam tomorrow .. and i think i can pass. thanks for this ..
I know this is too late but uh. Did you pass?
Thx so much for this explanation. Very clear and helpful.
Awesome to hear. You are welcome :)
Great explanations. Thank you
Explained well. Thank you.
So good👍well done!
Thanks for simplifying this
you made my life easier thank you!
Nice and simply put. Would anyone explain (In simple terms) what effect taking the natural logarithm of a scale that has a high kurtosis value.
Nice Video ! Keep up the good work !
Very helpful. It is short and clear
I'm glad you liked it.
It helped me a lot. Thankyou .
very clear and helpful. Thanks
Thank you so much.you explain it in very clear manner.
Awesome to hear! Thanks for watching and taking the time to let me know.
Thank you. this is very helpful
Thank you! Very well explained:)
thanks. it's very helpful.
3:24 I'm pretty sure the reason why we have more positive skews than negative skews is because the majority of the numbers we work with are non-negative, meaning there's a lower bound, i.e. 0, but no upper bound. For example, if you're measuring the amount of time it takes for someone to take a test without time limitations, it's likely that there are going to be outliers, people who take a really long time.
interesting view, cleared my mind thanks
very well explained....
Wish me good look for my Exam at 9.30AM and its already 3AM.
Your content is really helping.
Have not attended a single class for the subject. Wish me luck guys.
Good luck! In my opinion attendance does not equal learning .... hopefully you were able to learn in other ways.
Thakyou.
Can you discuss, different methods of sample size estimation. In your next video
Great video, Thanks
very nicely done
Hi, your video is good..Can I use this one for my multi-media studies?
Verry well done!
Hi, great video! So when the distribution is said to have fat tails, that means it is Leptokurtic?
Thanks.. Great video... You talk a little fast though, but you are clear and have a great voice.
Excellent! Thank you!
Thanks.. it is helpful
if the kurtosis is leptokurtic, I am more likely to get an expected random variable than in the case of any other distribution, am I right?
thanks!
Good work
Thanks for this. I kept coming across these terms and just could not understand the 'fat tail' analogy!
Thanks from Brazil! Obrigada! :)
You Are welcome
Thank you very much. Very informative
+bryan greenwood you are welcome. I'm glad you enjoyed it.
Excellent !! Very helpful !!
I'm happy it helped :)
hi. very nice. but i hav problem with my research data that skewness touches -2 . can u help me out with this issue? and what does it mean
Excellent thanks.
what about a non symmetrical bimodal graph, how would you decide if it is positive or negatively skewed?
Well explained.... thanks
+Sudha K you are welcome
holy moly, helps a lot! taking statistics online!!
+Kristania good to hear
Thank you so much!! you are awesome :)
Many thanks. :) Thought it would be better if you show us how to calculated the skewness and kurtosis. Its my topic to discuss.
i have a report tomorrow about this. It help me allot. Thanks again.
+Player Gabriel our students don't need to calculate it, which is why I didn't include it. Sorry!
NurseKillam you had a nice video, a superb one......1000likes goes to you...we need more about statistics as you did it
Happy you liked it :)
جزاك الله خيرا، Thank you