Math Problem Statement

In looking at this grouping of salaries, what salary might be expected for an open position based on the mean of these listed? Sometimes, the median can generate a different expectation for the salary an employee can expect when working at a position in the corporation. What is the median salary for the salaries listed above?

Solution

Let’s solve the two questions based on the provided salaries.

The salaries of the 10 employees are:

  • Brandon: $45,000
  • Robert: $58,000
  • Chloe: $62,000
  • Andrew: $59,000
  • David: $70,000
  • Tanya: $84,000
  • Rodney: $49,000
  • Sally: $67,000
  • Manuel: $78,000
  • Alexis: $68,000

1. Mean Salary Calculation:

The mean (average) is found by summing all the salaries and dividing by the number of employees.

Mean=45,000+58,000+62,000+59,000+70,000+84,000+49,000+67,000+78,000+68,00010\text{Mean} = \frac{45,000 + 58,000 + 62,000 + 59,000 + 70,000 + 84,000 + 49,000 + 67,000 + 78,000 + 68,000}{10}

Sum=640,000\text{Sum} = 640,000

Mean=640,00010=64,000\text{Mean} = \frac{640,000}{10} = 64,000

So, the mean salary is $64,000.


2. Median Salary Calculation:

To find the median, we first arrange the salaries in ascending order:

45,000,49,000,58,000,59,000,62,000,67,000,68,000,70,000,78,000,84,00045,000, 49,000, 58,000, 59,000, 62,000, 67,000, 68,000, 70,000, 78,000, 84,000

Since there are 10 values (even number), the median will be the average of the 5th and 6th salaries.

Median=62,000+67,0002=129,0002=64,500\text{Median} = \frac{62,000 + 67,000}{2} = \frac{129,000}{2} = 64,500

So, the median salary is $64,500.


Answer Choices:

  • Mean: $64,000
  • Median: $64,500

Thus, the correct answer to select is:
"Mean: $64,000, Median: $64,500"


Do you need further clarifications?
Here are 5 related questions for practice:

  1. What does the mean tell you about the data distribution?
  2. What happens to the mean if the highest salary increases by $10,000?
  3. Why is the median a better measure when there are outliers?
  4. What is the range of the salaries in this list?
  5. How would the mode be useful in this dataset?

Tip: Use the median when you want to minimize the effect of extreme values in the dataset.

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Math Problem Analysis

Mathematical Concepts

Mean Calculation
Median Calculation

Formulas

Mean = (Sum of all values) / (Number of values)
Median for even set = (Middle value 1 + Middle value 2) / 2

Theorems

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Suitable Grade Level

Grades 7-9