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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
Why you prefer normal distribution over other distributions in statistics?
we prefer normal distribution over other distribution in statistics because most of the data around us is continuous. So, for continuous data normal distribution is used.
What is a normal data set?
A normal data set is a set of observations from a Gaussian distribution, which is also called the Normal distribution.
What Percent of data is below the mean in a normal distribution?
In the normal distribution, the mean and median coincide, and 50% of the data are below the mean.
What percentage of the data in a normal distribution is represented by 1 SD of a sample?
Assuming that we have a Normal Distribution of Data, approx. 65% of the data will fall within One Sigma.
What does the normal allow you to measure?
The normal distribution allows you to measure the distribution of a set of data points. It helps to determine the average (mean) of the data and how spread out the data is (standard deviation). By using the normal distribution, you can make predictions about the likelihood of certain values occurring within the data set.
What is symmetrical normal distribution?
The Normal distribution is, by definition, symmetric. There is no other kind of Normal distribution, so the adjective is not used.
Can normal distridution apply on discrete data?
Yes, If you have a large data set, you can approximate the discrete data by Normal distribution (which is continuous). An example would be, "A coin is tossed 1000 times. What is the probability of rolling between 300 and 400 heads?" This problem, usually solved by Binomial distribution (which is a discrete distribution), is very difficult to solve because of the large data set and can be approximated by the Normal distribution.
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.
What is the mean of the sampling distribution of the sample mean?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
What is the sampling distribution of sample means and why is it useful?
Frequently it's impossible or impractical to test the entire universe of data to determine probabilities. So we test a small sub-set of the universal database and we call that the sample. Then using that sub-set of data we calculate its distribution, which is called the sample distribution. Normally we find the sample distribution has a bell shape, which we actually call the "normal distribution." When the data reflect the normal distribution of a sample, we call it the Student's t distribution to distinguish it from the normal distribution of a universe of data. The Student's t distribution is useful because with it and the small number of data we test, we can infer the probability distribution of the entire universal data set with some degree of confidence.
When your sample data is all negative values how can you convert it for use on a normal distribution?
The data from a normal distribution are symmetric about its mean, not about zero. There is, therefore nothing strange about all the values being negative.
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.
