Concept explainers
(a)
To find: the result of the mean salary and median salary if the teacher receives high salary.
(a)
Answer to Problem 22E
The new median of the salary is 1.05 times of the old median of the salary and the new mean salary is 1.05 times of the old mean salary.
Explanation of Solution
Given:
Teacher receives a 5% raise instead of a flat $1000 raise.
The
Calculation:
As each teacher receives a 5% raise, the new mean and median are obtained as follows:
Therefore the new mean salary is 1.05 times of the old mean salary.
We know that change of scale does not affect the median position. So the new median of the salary is the value of the old median salary raise by 5%. That means
Therefore the new median of the salary is 1.05 times of the old median of the salary.
Conclusion:
Therefore, the new median of the salary is 1.05 times of the old median of the salary and the new mean salary is 1.05 times of the old mean salary.
(b)
To explain:whether there will be increase inIQR and the standard deviation if there is a 5% raise.
(b)
Answer to Problem 22E
The new inter-
Explanation of Solution
Calculation:
As each teacher receives a 5% raise, the new standard deviation is obtained as follows:
Therefore the standard deviation of the new salary is 1.05 times of the old salary's standard deviation.
The first and third
Thus
Thus the new inter quartile range is obtained as follows:
Conclusion:
Therefore the new inter-quartile range is 1.05 times of the old inter-quartile range and the standard deviation of the new salary is 1.05 times of the old salary's standard deviation.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Statistics for Psychology
Basic Business Statistics, Student Value Edition (13th Edition)
Introductory Statistics (2nd Edition)
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Basic Business Statistics, Student Value Edition
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