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What does it mean when data is normally distributed?
It means that the data are distributed according to a probability distribution function known as the normal distribution. This site is useless for showing most mathematical functions but you can Google "normal distribution" to get more details.
Why does a researcher want to go from a normal distribution to a standard normal distribution?
A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.
State the main reason for using the empirical rule rather than chebyshevs theorem?
The empirical rule can only be used for a normal distribution, so I will assume you are referring to a normal distribution. Chebyshev's theorem can be used for any distribution. The empirical rule is more accurate than Chebyshev's theorem for a normal distribution. For 2 standard deviations (sd) from the mean, the empirical rule says 95% of the data are within that, and Chebyshev's theorem says 1 - 1/2^2 = 1 - 1/4 = 3/4 or 75% of the data are within that. From the standard normal distribution chart, the answer for 2 sd from the mean is 95.44% So, as you can see the empirical rule is more accurate.
What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
How is a frequency distribution used?
it is used to find mean<median and mode of grouped data
