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Does the median have 50 percent of the cases below only in a normal distribution?
No. By definition of the median, the median has 50 percent of the case below and 50 percent of the cases above. This has nothing to do with the cases being in a normal distribution.
In a standard normal distribution about percent of the scores fall above a z-score of 3.00?
0.13
What is the difference between minimum and lower quartile?
Consider the data: 1, 2, 2, 3, 4, 4, 5, 7, 11, 13 , 19 (arranged in ascending order) Minimum: 1 Maximum: 19 Range = Maximum - Minimum = 19 - 1 = 18 Median = 4 (the middle value) 1st Quartile/Lower Quartile = 2 (the middle/median of the data below the median which is 4) 3rd Quartile/Upper Quartile = 11 (the middle/median of the data above the median which is 4) InterQuartile Range (IQR) = 3rd Quartile - 1st Quartile = 11 - 2 = 9
What would -2 standard deviation below the mean be?
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
Under what circumstances would a score that is located 5 points above the mean be considered relatively close to the mean?
The answer depends on the underlying distribution and variability in the observations. For example, if the distribution is negatively skewed then 5 points above the mean is much more significant than 5 points below the mean. Next, looking at variablity: if almost all the scores are within -1 and +1 of the mean, then a score of 5 points above the mean is very significant but if the variance is 25, for example, then 5 points above the mean is one standard deviation from the mean: for a Normal distribution around a third of the observations would be further away - that is no big deal and so a score of mean+5 would be considered relatively close to the mean.
