Z score approximation ?
How do you approximate a z score when you have something like 2.3756Additional Details: how do you interlope ?
MarkFL said:Hello Zero,
Consulting a table, we find that the $z$-score associated with an area of 2.37 is 0.4911 and for an area of 2.38 is 0.4913.
To interpolate, we may simply use the ratio:
\(\displaystyle \frac{2.38-2.37}{0.4913-0.4911}=\frac{2.3756-2.37}{\Delta z}\)
\(\displaystyle \frac{0.01}{0.0002}=\frac{0.0056}{\Delta z}\)
\(\displaystyle 50=\frac{7}{1250\Delta z}\)
\(\displaystyle \Delta z=\frac{7}{62500}=0.000112\)
And so, we may state:
\(\displaystyle z\approx0.4911+\Delta z=0.491212\)
Using numeric integration, we find:
\(\displaystyle z=\frac{1}{\sqrt{2\pi}}\int_0^{2.3756}e^{-\frac{x^2}{2}}\,dx\approx0.49124\)
To Zero and any other guests viewing this topic, I invite and encourage you to register and post any other normal distribution question in our http://www.mathhelpboards.com/f23/ forum.
Best Regards,
Mark.
A z-score is a statistical measurement that indicates how many standard deviations a data point is above or below the mean of a dataset. It is important because it allows for the comparison of data points from different distributions and can help identify outliers.
A z-score can be calculated by subtracting the mean of a dataset from a data point and then dividing by the standard deviation. This formula can be written as (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.
Interpolation is a method of estimating unknown values based on known data points. In this case, it can be used to estimate the z-score of a data point that falls between two known z-scores. This is helpful when trying to calculate the z-score of a data point that does not have an exact value in the dataset.
The purpose of interpolating to find a z-score is to accurately estimate the z-score of a data point that falls between two known z-scores. This can help with statistical analysis and identifying outliers in a dataset.
Yes, a z-score can be negative if the data point is below the mean of the dataset. A negative z-score indicates that the data point is below the mean by a certain number of standard deviations.