standard error
A z-score cannot help calculate standard deviation. In fact the very point of z-scores is to remove any contribution from the mean or standard deviation.
There are two points of infection (the points where the curvature changes its direction) which lie at a distance of one standard deviation above mean and one standard deviation below mean.
The data point is close to the expected value.
The mean.The mean.The mean.The mean.
Your middle point or line for the plot (mean) would be 6.375. Then you would add/subtract 1.47 from your mean. For example, one standard deviation would equal 6.375 + 1.47 and one standard deviation from the left would be 6.375 - 1.47
The distance between the middle and the inflection point is the standard deviation.
A z-score cannot help calculate standard deviation. In fact the very point of z-scores is to remove any contribution from the mean or standard deviation.
No, standard deviation is not a point in a distribution; rather, it is a measure of the dispersion or spread of data points around the mean. It quantifies how much individual data points typically deviate from the mean value. A lower standard deviation indicates that the data points are closer to the mean, while a higher standard deviation indicates greater variability.
It's used in determining how far from the standard (average) a certain item or data point happen to be. (Ie, one standard deviation; two standard deviations, etc.)
The answer depends on the value of the new point. If the new value is near the mean then the new standard deviation (SD) will be smaller, if it is far away, the new SD will be larger.
There are two points of infection (the points where the curvature changes its direction) which lie at a distance of one standard deviation above mean and one standard deviation below mean.
Yes. Standard deviation depends entirely upon the distribution; it is a measure of how spread out it is (ie how far from the mean "on average" the data is): the larger it is the more spread out it is, the smaller the less spread out. If every data point was the mean, the standard deviation would be zero!
The data point is close to the expected value.
The mean.The mean.The mean.The mean.
The standard deviation itself is a measure of variability or dispersion within a dataset, not a value that can be directly assigned to a single number like 2.5. If you have a dataset where 2.5 is a data point, you would need the entire dataset to calculate the standard deviation. However, if you are referring to a dataset where 2.5 is the mean and all values are the same (for example, all values are 2.5), then the standard deviation would be 0, since there is no variability.
In essence, it's because a single data point provides no information about the dispersion of the population from which it was drawn. If you look at the definition of the t statistic you will notice that there is an estimator of of the population standard deviation in its denominator (in other words, the population's dispersion). Without at least two data points this estimator cannot be calculated. Think about it another way. If you have many observations you have a good idea how 'closely' they are distributed. The fewer you have the less information is available.
Your middle point or line for the plot (mean) would be 6.375. Then you would add/subtract 1.47 from your mean. For example, one standard deviation would equal 6.375 + 1.47 and one standard deviation from the left would be 6.375 - 1.47