Incomes, rounded to the nearest $1,000, from 2 different socioeconomic groups of 10 members each were collected and are presented below. GROUP 1 INCOME GROUP 2 INCOME Member 1 $25,000 Member 1 $27,000 Member 2 $29,000 Member 2 $38,000 Member 3 $18,000 Member 3 $45,000 Member 4 $31,000 Member 4 $41,000 Member 5 $22,000 Member 5 $36,000 Member 6 $22,000 Member 6 $24,000 Member 7 $12,000 Member 7 $62,000 Member 8 $33,000 Member 8 $41,000 Member 9 $45,000 Member 9 $39,000 Member 10 $38,000 Member 10 $48,000 Which is the best measure of central tendency for these groups? a) The mode b) The mean c) None of the above d) All are equal e) The median
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.
Incomes, rounded to the nearest $1,000, from 2 different socioeconomic groups of 10 members each were collected and are presented below.
GROUP 1 INCOME GROUP 2 INCOME
Member 1 $25,000 Member 1 $27,000
Member 2 $29,000 Member 2 $38,000
Member 3 $18,000 Member 3 $45,000
Member 4 $31,000 Member 4 $41,000
Member 5 $22,000 Member 5 $36,000
Member 6 $22,000 Member 6 $24,000
Member 7 $12,000 Member 7 $62,000
Member 8 $33,000 Member 8 $41,000
Member 9 $45,000 Member 9 $39,000
Member 10 $38,000 Member 10 $48,000
Which is the best measure of
Group 1 Group 2
Mean: $27,500 $40,100
Median: $27,000 $40,000
Mode: $22,000 $41,000
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