The following represent statistics of weekly salaries at the Harper Publishing Company.
Mean = $470 Median = $475 Mode = $460 Standard deviation = $30
First Quartile = $450 Third Quartile = $485 79th Percentile = $545 P67 = $483

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

Step-by-step 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

I hope you have a SUPER day!

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