The stem-and-leaf display shows populations of the 50 regions, in millions of people, according to a census. Complete parts a through d below. 5 1 99 10111344 0 5555566667777789 0 11111222222223334444444 (2 |5 means 25) a) What measures of center and spread are most appropriate? For the center, use the median because the distribution is not symmetric. For the spread, use the IQR because the distribution is not symmetric. b) Without doing any calculations, which must be larger: the median or the mean? Explain. The mean is larger because the distribution is skewed to the right. c) From the stem-and-leaf display, find the median and the interquartile range. The median is 5 million. (Simplify your answer.) The interquartile range is 6 million. (Simplify your answer.) d) Write a few sentences describing this distribution. This distribution has more than 2 obvious modes, so it is multimodal. In this case, the right tail is longer and the distribution is approximately symmetric. There is/are at least one obvious outlier.
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.
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