Normal Distribution Graphs

Original post by CoolCavy

Hey guys

A picture of the graphs may help but I think I can see them in my head from what you've described :hugs:

What do the x and y axis represent on those graphs? (This should help you to explain the difference)

Reply 2

Original post by SeanFM

A picture of the graphs may help but I think I can see them in my head from what you've described :hugs:

What do the x and y axis represent on those graphs? (This should help you to explain the difference)

hey sean, i tried to draw them :redface:

and the x and y have no values, we were just given those two graphs and it says 'how would you describe the difference between these curves?' x

Reply 3

undercxver

You can use these names to search it?

I'm guessing you have to describe how distributed the data is away from the mean. :s:

Reply 4

Original post by CoolCavy

hey sean, i tried to draw them :redface:

and the x and y have no values, we were just given those two graphs and it says 'how would you describe the difference between these curves?' x

even in Maths you are doing art :borat:

For this question you don't need to know what the particular x and y values are, but knowing what they represent in general would help.

Here's an image of the standard normal distribution (mean 0, variance 1):

What do the x and y values represent here?

In your sketches they will represent the same thing, just not the same numbers.

Reply 5

ChristianNewman

Maybe the variance on the thinner distribution graph is less? (Guess)

Reply 6

Original post by undercxver

You can use these names to search it?

I'm guessing you have to describe how distributed the data is away from the mean. :s:

Oh thank you for that! now at least i can label it and try to google :hugs:

Original post by SeanFM

even in Maths you are doing art :borat:

What do the x and y values represent here?

In your sketches they will represent the same thing, just not the same numbers.

oh i forgot to say this was biology :colondollar:

but there is a mathsy overlap :yes:

(unfortunately for me :redface:

)
i honestly have no idea sean :redface:

the middle one is the median? :redface:

does that mean that the higher one will have a higher median? :redface:

Reply 7

Original post by ChristianNewman

Maybe the variance on the thinner distribution graph is less? (Guess)

hey

what is variance? :redface:

Reply 8

username1560589

Original post by CoolCavy

hey

what is variance? :redface:

The square of standard deviation.

Reply 9

undercxver

Original post by CoolCavy

Oh thank you for that! now at least i can label it and try to google :hugs:

x

i honestly have no idea sean :redface:

the middle one is the median? :redface:

does that mean that the higher one will have a higher median? :redface:

* σ means standard deviation.

These show that 68% of the data lies within 1σ.
These show that 95% of the data lies within 2σ.
These show that 99.7% of the data lies within 3σ.

If there is a leptokurtic distribution then the data is spread closer to the mean than a platykurtic distribution.

I hope I am making sense. :redface:

Reply 10

Original post by morgan8002

The square of standard deviation.

sorry i must seem so thick rn but i'm not entirely sure what standard deviation is either apart from the fact that it shows how far away values are from the mean but we havent really gone into it in that much detail in biology yet :redface:

-----
@SeanFM here is what i put from what i could gather :colondollar:

:
The wider lower graph (platykurtic, ty @undercxver) is shaped accordingly as the points are highly dispersed resulting in a lower peak than a normal distribution and the points are less clustered around the mean. I then put the inverse for the leptokurtic one. Ngl i don't really get what i have written but hopefully she will go over it with us or if not i'll go and see her about this whole graph thing :redface:

Reply 11

samb1234

Original post by CoolCavy

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@SeanFM here is what i put from what i could gather :colondollar:

One thing that might help you to get the shape is to remember that the area under the curve must =1 (since total probabilities must sum to 1) so if you have a lower peak the rest of the distribution must compensate for that so essentially you will get a fatter middle section that doesn't tail off as rapidly away from the centre

Reply 12

Original post by CoolCavy

-----
@SeanFM here is what i put from what i could gather :colondollar:

Yeah that's right, but I'm sure you can word it in an easier way to understand (for you and whoever is reading the answer :tongue:

)

I don't know if you've seen a standard normal graph before (the one I showed you) but the z values there represent some other x value (like an independent variable) and each one of those has a corresponding z value (the 'x axis' on that graph is made up of numbers which are measured in z instead of x) so z=0 is the point in the middle. And the y axis represents the probability of that value happening.

Eg if something is distributed normally with mean 10 and variance 4, then let's write that as X~N(10,4), and for each value of X you can find a corresponding Z value by doing X-mean/(standard deviation), so the z value for X=10 is 0, the z value for 12 is 1, the z value for 9 is -0.5 etc and you know the shape of the z (standard normal) distribution and and that the probability of z=0 is the highest (so this corresponds to the X value 10, and we can interpret this as 10 being the most common number that you'll get if you get millions of values of X).

But that's just an aside - the point is that the x axis on those distributions represent some values from a sample or whatever, and the y values represent the probability of each of those values happening on their own. So if one graph is taller and thinner than the other, then you can compare the range of values on the x axis (and so how many different points you can get in your sample) and the probability of getting those points, compared to something that is shorter (so everything has a relatively smaller chance of happening but you can get more x values as a result).

Reply 13

thank you to everyone who has posted so far :smile:

you are all helping :yes:

sorry to be annoying but @SeanFM
how would you work out the standard deviation of 22 with an average of 28.9?

so far i have:
22 - 28.9 = 0.7612456747
and then i squared it but it gave a tiny number :s-smilie:

Reply 14

username1560589

Original post by CoolCavy

The standard deviation is a measure of the spread from the mean. It's related to the average distance to the mean. It's denoted by

\sigma

.

There's a fairly simple formula for the standard deviation of a sequence of n numbers, which you can Google if you want.

In this case we aren't talking about a finite set though. The normal distribution takes values of x all along the number line, so standard deviation and variance have to be defined a little more complicated. It's the same idea though. Standard deviation and its square, variance can be used to check how spread out the values are.

A probability distribution function takes a value of x and has a rule to calculate the probability density at x(basically the probability of x). If you draw the graph of the function then you get the x values on the x axis and the probability density on the y axis. If the graph is high at a point then it's likely that a randomly chosen x will be there. The area of the graph is always 1. If the graph is high at one point and low everywhere else then it has a low standard deviation(and hence low variance and spread). If it's more spread out then it has a high spread.

The normal distribution is one family of probability distribution functions, which has an equation that you can Google if you want. This equation allows you to calculate the probability density for a particular value of x. The more their standard deviations, the shorter and longer their graphs look.

Reply 15

Original post by CoolCavy

thank you to everyone who has posted so far :smile:

you are all helping :yes:

There doesn't seem to be enough information there :tongue:

does it give you what the probability of getting 22 is?

Reply 16

Original post by SeanFM

There doesn't seem to be enough information there :tongue:

does it give you what the probability of getting 22 is?

well the exact question is 'calculate the standard deviation for the first two sets of data'

set 1:
22

24

average = 28.9

set 2:
19

22

average = 20.8

:redface:

i googled the formula and it has this bottom bit about square rooting and all that :s-smilie:

urgh fml i can't do maths :/

Reply 17