Question

the basketball star
diagnostic
the employees at two small companies have their annual salaries listed in the table below.
if you were a typical employee, at which company do you think you could expect to make more money? explain your answer.

Explanation:

Step1: Calculate the median for Company X

First, sort the salaries of Company X: \(25000,27000,28000,32000,33000,35000,36000,37000,38000,129000\). There are \(n = 10\) values. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\), \(\frac{n}{2}+1 = 6\). The median \(M_X=\frac{33000 + 35000}{2}=34000\)

Step2: Calculate the median for Company Y

Sort the salaries of Company Y: \(28000,30000,31000,35000,36000,38000,39000,40000,41000,42000\). There are \(n = 10\) values. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\), \(\frac{n}{2}+1=6\). The median \(M_Y=\frac{36000+38000}{2} = 37000\)

Answer:

A typical employee (represented by the median - since the data for Company X has an outlier \(129000\) which skews the mean) would expect to make more money at Company Y. The median salary of Company X is \(34000\) and the median salary of Company Y is \(37000\)