A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is? (a) The mean is affected by the skewness, whereas the median is not. (b) The median is always the preferred statistic. (c) The mean will be less than the median when the data are strongly skewed to the right. (d) The mean should be used only when data are strongly skewed to the left.
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.
A local real estate magazine used the
reported the SAT score of the average student who attends Groveland High
School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is?
(a) The mean is affected by the skewness, whereas the median is not.
(b) The median is always the preferred statistic.
(c) The mean will be less than the median when the data are strongly skewed to the right.
(d) The mean should be used only when data are strongly skewed to the left.
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