Question

a small company pays annual salaries to its employees as shown in the table. 13 employees with a salary of $20,900 10 employees with a salary of $23,100 18 employees with a salary of $26,600 3 employees with a salary of $31,600 4 employees with a salary of $37,500 1 employee with a salary of $149,900 find the mean, median and mode salary for the employees. the mean salary for the employees is $ (type a whole number. round to the nearest hundred as needed.)

Explanation:

Step1: Calculate total number of employees

$13 + 10+18 + 3+4 + 1=50$

Step2: Calculate total salary

$13\times20900+10\times23100 + 18\times26600+3\times31600+4\times37500+1\times149900$
$=271700+231000+478800+94800+150000+149900$
$=1376200$

Step3: Calculate the mean

Mean $=\frac{1376200}{50}=27524$

Step4: Find the median

Since there are 50 (an even - numbered) employees, the median is the average of the 25th and 26th ordered salaries.
First, order the number of employees: 13 employees with $20900$, then 10 employees with $23100$, then 18 employees with $26600$.
The 25th and 26th values fall within the group of employees with a salary of $26600$, so the median is $26600$.

Step5: Find the mode

The mode is the salary that appears most frequently. The salary of $26600$ has 18 employees, which is the highest frequency among all salaries, so the mode is $26600$.

Answer:

Mean: $27524$
Median: $26600$
Mode: $26600$