n 2007 the New York Times reported that the median annual household income in the UnitedStates was $55,500 (New York Times website, August, 21, 2013). Answer the followingquestions based on the following sample of 14 household incomes for 2013 ($1000s).49.4 52.4 53.4 51.3 52.1 48.7 52.152.2 64.5 51.6 46.5 52.9 52.5 51.2a. What is the median household income for the sample data for 2013?b. Based on the sample data, estimate the percentage change in the median householdincome from 2007 to 2013.c. Compute the first and third quartiles.d. Provide a five-number summary.e. Using the z-score approach, do the data contain any outliers? Does the approach thatuses the values of the first and third quartiles and the interquartile range to detect outliers provide the same results?
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.
n 2007 the New York Times reported that the
States was $55,500 (New York Times website, August, 21, 2013). Answer the following
questions based on the following sample of 14 household incomes for 2013 ($1000s).
49.4 52.4 53.4 51.3 52.1 48.7 52.1
52.2 64.5 51.6 46.5 52.9 52.5 51.2
a. What is the median household income for the sample data for 2013?
b. Based on the sample data, estimate the percentage change in the median household
income from 2007 to 2013.
c. Compute the first and third
d. Provide a five-number summary.
e. Using the z-score approach, do the data contain any outliers? Does the approach that
uses the values of the first and third quartiles and the
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