Finding the Mean/Median of a Normally Distributed Curve

[cns]

I am given that the lowest value on a graph is 0 and that it's SD is 20, but I need to find the mean? How would I do that? I would think to use the Z-test formula but I keep getting 0 which is wrong for sure since 0 is the lowest value of the graph

Thanks

 

[CRGreathouse]

You can't get it with that amount of information.

 

[cns]

I was thinking that since the lowest x value is 0 and we know that the SD is 25 isn't there some way to figure out using the SD how far away the mean (midpoint) is from 0?

thanks

 

[SW VandeCarr]

I was thinking that since the lowest x value is 0 and we know that the SD is 25 isn't there some way to figure out using the SD how far away the mean (midpoint) is from 0?

thanks

Only if the distribution is the Standard Normal. In that case, the mean is 0 and and the SD is 1. However, the normal (Gaussian) distribution has infinite tails so there is no "lowest" probability value. You would need to assign your 0 data value a probability density assuming the Standard Normal Distribution, and then substitute your own data values.

 

[Reyzal]

I don't think you can technically get the answer Although; I know what you may be thinking of.

68% of data is in the first SD of the mean, 95% of data is within 2 standard deviations, and 99.7% of data is within 3.

So unless they want you to guess its about 60 as the mean, I don't think you can get it, cause technically .15% of data would still be lower than 0 if mean was 60


Wiki info cause I've only learned stats through self learning:
If a data distribution is approximately normal then about 68% of the data values are within 1 standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95% are within two standard deviations (μ ± 2σ), and about 99.7% lie within 3 standard deviations (μ ± 3σ). This is known as the 68-95-99.7 rule, or the empirical rule.

 

[SW VandeCarr]

The OP has a data point and a value for the SD. If a probability density can be assigned to the data point and one assumes a standard Gaussian PDF, why couldn't the OP estimate the mean (which would also be the median in the standardized normal distribution)?

 

[ych22]

The OP has a data point and a value for the SD. If a probability density can be assigned to the data point and one assumes a standard Gaussian PDF, why couldn't the OP estimate the mean (which would also be the median in the standardized normal distribution)?

Actually you and Reyzal are both right for different reasons. I think OP did not provide all the details required to solve the question. I believe we need the total number of data points to provide an answer.

 

[SW VandeCarr]

Actually you and Reyzal are both right for different reasons. I think OP did not provide all the details required to solve the question. I believe we need the total number of data points to provide an answer.

The OP provided a known SD and a data point x. I stipulated that we must know:

$$p(x\leq a)$$ the probability of a value x equal or less than 'a' (probability density). The OP gave a=0 and SD=20. We assume a SND with monotonically increasing values of x plotted against $$F(x)=p(x\leq a)$$. Say for the sake of a demonstration that x are temperatures in deg Celsius. We know that $$F(x)=p(x\leq 0)$$ Let G(F(x)) = Z. Than if

F(x)<0.5: $$a+G(F(x))\sigma=\mu$$

F(x)=0.5: $$a=\mu$$

F(x)>0.5: $$a-G(F(x))\sigma=\mu$$

So if G(F(x))= 0.50 and F(x)<0.5 then the mean is 0+0.5(20)= 10 deg C

EDIT: cns: I just wanted to show a specific circumstance where you could estimate the mean with one zero value data point and a known SD. In general you can't. If you have a discrete variable with a non-zero probability for a zero valued data point you will usually need all the data to calculate an estimate of say $$\lambda$$ of a Poisson distribution.