the given table shows the hourly wages for groups of employees based on the number of years working for a…

the given table shows the hourly wages for groups of employees based on the number of years working for a business and how many employees are in each group.\nemployee wages\n| hourly wage | employees |\n| ---- | ---- |\n| $13.00 | 6 |\n| $14.00 | 4 |\n| $15.00 | 7 |\n| $16.00 | 3 |\nall employees are given a 10% raise. with this raise, by how much does the median hourly wage change?\na. $1.35\nb. $1.40\nc. $1.45\nd. $1.50

the given table shows the hourly wages for groups of employees based on the number of years working for a business and how many employees are in each group.\nemployee wages\n| hourly wage | employees |\n| ---- | ---- |\n| $13.00 | 6 |\n| $14.00 | 4 |\n| $15.00 | 7 |\n| $16.00 | 3 |\nall employees are given a 10% raise. with this raise, by how much does the median hourly wage change?\na. $1.35\nb. $1.40\nc. $1.45\nd. $1.50

Answer

Explanation:

Step1: Calculate total number of employees

$6 + 4+7 + 3=20$ (employees)

Step2: Find the position of the median

Since $n = 20$ (even), the median is the average of the $\frac{n}{2}=10$th and $(\frac{n}{2}+ 1)=11$th ordered - values.

Step3: Determine the original median

Ordering the data by number of employees: First 6 employees have a wage of $13$, next 4 have a wage of $14$. So far, we have accounted for $6 + 4=10$ employees. The 10th - value is $14$ and the 11th - value is $15$. The original median is $\frac{14 + 15}{2}=14.5$.

Step4: Calculate the new hourly - wage after a 10% raise

New wage formula: $New\ wage=Original\ wage\times(1 + 0.1)$. For $13$, new wage is $13\times1.1 = 14.3$; for $14$, new wage is $14\times1.1=15.4$; for $15$, new wage is $15\times1.1 = 16.5$; for $16$, new wage is $16\times1.1=17.6$.

Step5: Find the new median

The 10th - value is $15.4$ and the 11th - value is $16.5$. The new median is $\frac{15.4+16.5}{2}=15.95$.

Step6: Calculate the change in median

Change in median = New median−Original median. So, $15.95−14.5 = 1.45$.

Answer:

C. $1.45$