(i Ogive (i) Ogive Showing Cumalative Fercentage of Data Persoral kcone per Capita by State Personal hcome per Capta by Siate 100% 50 49 100 40+ 6 30+ 60+ 20+ 16 40+ 10+ 20+ 0% 27,5 325 37,5 42,5 47,5 52,5 275 32,5 37,5 42,5 47,5 52,5 Per cepila inoame ($1000) Balary (1000) Cumulatve tequency Percent of states
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.
Interpretation The ogives shown are based on U.S Census data and show the average
annual personal income per capita for each of the 50 states. The data are rounded to
the nearest thousand dollars.
(a) How were the percentages shown in graph (ii) computed?
(b) How many states have average per capita income less than 37.5 thousand dollars?
(c) How many states have average per capita income between 42.5 and 52.5 thousand
dollars?
(d) What percentage of the states have average per capita income more than 47.5
thousand dollars?
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