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A negative z score always indicates that the raw score is below the mean?
In general, the answer is no, both negative and positive z score values should be expected. A z-score (or standardize score) is the raw data value minus the mean an…d then this result divided by the standard deviation. If the data can be considered normally distributed and a random sample is taken from a population, then as the sample size becomes large, approximately half the z-scores should be negative and half of the z-scores should be positive. There are some exceptions. Small data sets may have only positive values. A non-normal (skewed) distribution if skewed to the right, may have, after normalizing, may have a higher portion of z scores as positives.
Let your raw score be x and M the mean and S the standard deviation. The Z score for your specific x is Z=(x-M)/S So say your score is 80 (out of 100) and the mean is 70 an…d the standard deviation is 10. Then the z score for your 80 is: (80-70)/10=1 If on the other hand you got a 60, then the z score would be -1.
It means that it is less than the mean.
Without more information you cannot.
The one-tailed z-value is: P(Z < z) = 0.9693 => z = 1.8706
Yes. However, because the distribution is symmetric about 0, some tables give only positive values for z.
It means that your raw score is four standard deviations below the mean. This will mean different things depending on the context of the question. If you're looking at the pro…bability of a single score occurring in a given distribution (say, a score of 40 in a distribution of scores with a mean of 80 and a std. dev. of 10), then this means that the probability of getting a 40 is very, very low--less than .00002.
z = (x - μ) / σ is the formula where x is the raw score and z is the z-score. μ and σ are the mean and standard deviations and must be known numbers. Multiply both sides… by σ zσ = x-μ Add μ to both sides μ + zσ = x x = μ + zσ You calculate the raw score x , given the z-score, μ and σ by using the above formula.
Yes. The z or Standard Normal distribution is symmetric about the value z = 0.
z-score of a value=(that value minus the mean)/(standard deviation). So if a value has a negative z-score, then it is below the mean.
There is not enough information to answer your question. To determine a Z-Score, the mean and standard deviation are also required.
A percentile is always between 0% and 100%, never negative.
A negative z-score indicates that the observed value (or statistic) was below the mean. In non-directional tests, a negative z-score is just as likely as a positive one.
Go back to the basic data, estimate the sample mean and the standard error and use these to estimate the Z-score.
The Gaussian (Normal) distribution is determined by two parameters: its mean and its variance. Each combination of these two parameters results in a different probability dens…ity function (pdf). Finding the probability based on raw scores would require values of the pdf relating to that particular combination of mean and variance. The pdf for the Gaussian distribution is not simple to calculate and it would be impossible to tabulate infinitely many of them. Instead, only the pdf for the Z-scores - the Standard Normal pdf - is tabulated. Any raw score is converted to a Z-score and the probability evaluated from the tables.