Class Median Age Midpoint, x Income, / 15-24 years 19.5 $10,869 25-34 years 29.5 $34,113 35-44 years 39.5 $45,225 45-54 years 49.5 $46,466 55-64 years 59.5 $42,176 65 years and older 69.5 $27,612
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.
An individual’s income varies with his or her age. The following table shows the median income I of males of different age groups within the United States for 2012. For each age group, let the class midpoint represent the
independent variable, x. For the class “65 years and older,” we will assume that the class midpoint is 69.5.
(a) Use a graphing utility to draw a
data. Comment on the type of relation that may exist
between the two variables.
(b) Use a graphing utility to find the quadratic
best fit that models the relation between age and median
income.
(c) Use the function found in part (b) to determine the age at
which an individual can expect to earn the most income.
(d) Use the function found in part (b) to predict the peak
income earned.
(e) With a graphing utility, graph the quadratic function of
best fit on the scatter diagram.
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