Consider the four pairs of dotplots. Each dotplot represents a set of measurements. For which pairing is the standard deviation corresponding to the dotplot on the right greater than the dotplot on the left? (A) (B) (C) (D) .......
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
When we observe at pairs of dotplots, the one with the higher standard deviation will display data that are more spread out from its mean.
In Option (C) we can see that the dotplot on the right has a mean at 3.5 with the rest of the data spread equally on the right and on the left. The corresponding dotplot on the left in option (C) also has symmetry with data spread out equally on the right and on the left. However, the dotplot on the left has most of the data near the center, where the dotplot on the right has most of the data far from the center. More data that are far from the center means that there are more, larger deviations from the mean.
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