Density Curves and their Properties (5.1)

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Thank you for watching and supporting my channel :) More videos will be posted soon, they just take a long time to make

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Thank you very much John, I really appreciate you sharing it with others and for contributing. I am doing my very best to keep the videos coming!

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[@dr.allwyndsouza5246]

I thought about how can area under the curve be equal to proportion of total persons corresponding to a selected data set, im not able to digest this concept. Because if its relative frequency (length) X data set (width), relative frequency being unitless as it's a proportion, multiplying it with data set (weight) gives ans. in pounds , so how can it be percentage of persons in that data set ? Maybe im making a silly mistake. Please help me with this confusion.

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[@Simplelearningpro]

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[@Simplelearningpro]

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Thank you for your comment! Good luck with your studies Ahmed :)

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[@Simplelearningpro]

I'm glad! More videos to come. Thank you for your comment.

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[@Simplelearningpro]

You're welcome! Thanks for leaving a comment Paras :)

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Great video and explanation my friend. I wonder where is the video showing how to calculate this using an integral. Thanks for the amazing work.

[@sebastiancontrerasgonzalez7277]

5:56 In this particular case, the answer is 20% because proportions are represented by the height of the curve. Relative frequency isn't density. For computing density, the frequency has to be divided by the length of its bin.

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Thank you for leaving a comment :)

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Thanks alot this video gave me more understanding about the density curve!

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You're welcome! Good luck with the rest of your learning and thank you for leaving a comment :)

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Will do :) thank you for the comment!

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[@গোলামমোস্তফা-শ৮থ]

How total area of relative frequency distribution is one(1)? I tried to solve an example but it was not 1 at all. You can try your own example you mentioned here.

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Thank you! And I am trying my best. In the mean time, feel free to support me on patreon to help accelerate this process.

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Thank you :)

[@bigfigwasp8689]

What you said here is slightly wrong. 1:43 You said, "If we take the histogram we just worked with and if we draw a curve around its distribution we have essentially made a density curve". I know you put in the word "essentially" there and probably you know that it technically would NOT make a density curve. Sure the shape would remain the same (if the scales of the axes aren't changed) but the units along the y axis isn't relative frequency in a density curve. It is relative frequency per unit x, that's the frequency density, or the probability density and hence the name. That's why when you find the integral area it is dimensionally ((relative frequency per unit x) times x) which results in relative frequency hence total area is 1 because total relative frequency is 1. (Infact, the function along y in a density plot is not relative frequency. It is the first derivative of relative frequency with respect to x. Which is the probability density. Unit: relative frequency per unit x) 1:55 You were also wrong when you said, "like a relative frequency distribution, density curves always have an area that is equal to 1 or a 100%". If the x-intervals each have a width of 10 units the total area of a relative frequency distribution would be 10. For discrete relative frequency distributions like a histogram we can just look at the heights of the bars and know the relative frequencies, and yes, the heights add up to 1. But for a continuous distribution the total area adds up to 1 because the y unit isn't relative frequency but relative frequency per unit x. 5:49 Now, think how the example you gave towards the end of the video was wrong. When you find the area in a relative frequency vs weights graph, the area isn't relative frequency or probability. It is relative frequency times weight, which means practically nothing. You were wrong in the y-unit which will be relative frequency per weights. Yeah, that practically means nothing either, that's why heights don't mean anything in a density curve. Area matters. Which would become (relative frequency per unit weight) × weight = relative frequency Dude, I saved your playlist to my library and watched this video and got confused. You are influencing a lot of people by those fancy animations. Don't mix up the concepts in an attempt to make things too simple.

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[@ombie9439]

At 1:30.. how is total area under relative frequency distribution equal to 1? Shouldn't it be equal to 10?..It would be really helpful if someone would help me out🙏

[@bigfigwasp8689]

Yes, I think that as well. I have commented an elaborate explanation here. See if that helps you

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[@Simplelearningpro]

Doing my best to keep the content coming! Thank you for supporting my channel :)

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[@Simplelearningpro]

More videos will be coming soon!

[@aidenstonehouse9651]

You said that the area of a frequency density curve is always 1. Incorrect. The histogram you showed had an area far larger than 1. Do you mean relative frequency density?

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Yes

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[@Simplelearningpro]

Thank you so much for your comment Charan.

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