Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $60,000,mean salary = $140,000,median = $100,000,range = $240,000,IQR = $120,000,first quartile = $70,000,standard deviation = $80,000.
Suppose that business has been good and the company gives every employee a $10,000 raise.Give the new value of each of the summary statistics.
A)Minimum: 60,000;Mean: 140,000;Median: 100,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
B)Minimum: 70,000;Mean: 150,000;Median: 100,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
C)Minimum: 70,000;Mean: 140,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
D)Minimum: 70,000;Mean: 150,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
E)Minimum: 60,000;Mean: 150,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000

Question

Quizplus · Accepted Answer

We know that the minimum salary remains the same at $60,000. The mean salary increases by $10,000 for every employee, so it becomes $140,000 + $10,000 = $150,000. The median is not affected by a uniform raise, so it remains $100,000. The range is still $240,000. The IQR is determined by the difference between the third quartile and the first quartile, and since every employee received the same raise, there is no change to the quartiles. Therefore, the IQR remains $120,000 and the first quartile remains $70,000. The standard deviation is a measure of variability in the data, so it is not affected by a uniform raise. Therefore, the standard deviation remains $80,000. Of the given choices, option D matches all of these conditions.

Here Are the Summary Statistics for the Monthly Payroll for an Accounting