Answer:
1) The most common salary is $460.
2) The salary that half of the employees surpassed is $475
3) The percentage of employees with salaries below $485 is 75%
4) 75% of the employees have a salary above $450.
5) The salary that stands 3 standard deviations below the mean is $380
6) 33% of the employees have a salary above $483.
7) The salary that stands 2 standard deviations above the mean is $530
Explanation:
Hello!
1. What is the most common salary?______________
The measure that allows you to know which one is the most common value (i.e. the most frequent/observed number) in a data set is the mode. According to the given statistics, the most common salary is $460.
2. What salary did half the employees surpass?_________________
The measure that divides the sample in exactly a half (bottom 50% from the top 50%) is the median. In this example the salary that half of the employees surpassed is $475.
3. About what percent of employee's salaries is below $485?__________________
As you can see in the descriptive statistics, the third quartile (Q₃) is $485.
The Q₃ is the value that divides the bottom 75% of the sample from the top 25%. So the percentage of employees with salaries below $485 is 75%
4. What percent of the employees are above $450?___________________
The first quartile (Q₁) is the value that separates the bottom 25% of the sample from the top 75%. In this case Q₁= $450, which means that 75% of the employees have a salary above $450.
5. What salary is 3 standard deviations below the mean?____________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 3 standard deviations below the mean is
X[bar]-3S= $470-3*$30= $380
6. About what percent of employee's salaries is above $483?__________________
P₆₇= $483, this value is the 67th percentile and means that 67% of the employees have a salary below $483.
If 67% are below $483, then 100 - 67= 33% of the employees have a salary above $483.
7. What salary is 2 standard deviations above the mean?______________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 2 standard deviations above the mean is
X[bar]+2S= $470+2*$30= $530
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