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Can The standard deviation of a distribution be a negative value?
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
The national average SAT score is 1028 with a standard deviation of 92 Assuming a normal distribution what score corresponds to the 90th percentile?
124
Which is better a score of 92 on a test with a mean of 71 and a standard deviation of 15 or a score of 688 on a test with a mean of 493 and a standard deviation of 150?
score of 92
What a large standard deviation means?
A large standard deviation means that the data were spread out. It is relative whether or not you consider a standard deviation to be "large" or not, but a larger standard deviation always means that the data is more spread out than a smaller one. For example, if the mean was 60, and the standard deviation was 1, then this is a small standard deviation. The data is not spread out and a score of 74 or 43 would be highly unlikely, almost impossible. However, if the mean was 60 and the standard deviation was 20, then this would be a large standard deviation. The data is spread out more and a score of 74 or 43 wouldn't be odd or unusual at all.
If the mean is 3 and the standard deviation is 1 the z-score associated with a raw score of 4.5?
1.50
Can The standard deviation of a distribution be a negative value?
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
In a distribution with a standard deviation of eight an individual score of 42 corresponds to a Z score of -0.5. What is the mean of this distribution?
The mean is 46.
Why normality is required for standard deviation application?
Because the z-score table, which is heavily related to standard deviation, is only applicable to normal distributions.
What kind of distribution is a standard z distribution?
It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.
How do you use the z-score to determine a normal curve?
If the Z-Score corresponds to the standard deviation, then the distribution is "normal", or Gaussian.
What is the z score for a score of 75 if the mean of the distribution is 85 and the standard deviation is the distribution is 5?
z = (75 - 85)/5 = -10/5 = -2
A score of 0.60 standard deviation represents what score of percentile?
It depends on the underlying distribution. If Gaussian (standrad normal) then the percentile is 77.
What is the z score of 1.0?
It is the value that is one standard deviation greater than the mean of a Normal (Gaussian) distribution.
What is the difference between a z score and t score?
A z-score measures how many standard deviations an individual data point is from the mean of a population, assuming the population standard deviation is known and the sample size is large (typically n > 30). In contrast, a t-score is used when the sample size is small (n ≤ 30) or when the population standard deviation is unknown, relying on the sample's standard deviation instead. The t-distribution, which the t-score utilizes, is wider and has heavier tails than the normal distribution, reflecting more uncertainty in smaller samples. As sample sizes increase, the t-distribution approaches the normal distribution, making z-scores more applicable.
How do you find the mean from raw score z score and standard deviation?
To find the mean from a raw score, z-score, and standard deviation, you can use the formula: ( \text{Raw Score} = \text{Mean} + (z \times \text{Standard Deviation}) ). Rearranging this gives you the mean: ( \text{Mean} = \text{Raw Score} - (z \times \text{Standard Deviation}) ). Simply substitute the values of the raw score, z-score, and standard deviation into this formula to calculate the mean.
How do you calculate Z and T scores?
z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)
The national average SAT score is 1028 with a standard deviation of 92 Assuming a normal distribution what score corresponds to the 90th percentile?
124
