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A local travel office has 10 employees. Their monthly salaries are given below. \( \$ 1500, \$ 1710, \$ 1670, \$ 1140, \$ 1470, \$ 1560, \$ 1810, \$ 1380, \$ 3700, \$ 6400 \) (a) Find the mean. The mean is \( \$ \square \).

Ask by Mann Maxwell. in the United States
Jan 14,2025

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Answer

The mean salary is \$2234.

Solution

To find the mean of the monthly salaries of the 10 employees, we need to add up all the salaries and then divide by the total number of employees. Given monthly salaries: \( \$ 1500, \$ 1710, \$ 1670, \$ 1140, \$ 1470, \$ 1560, \$ 1810, \$ 1380, \$ 3700, \$ 6400 \) First, let's add up all the salaries: \( 1500 + 1710 + 1670 + 1140 + 1470 + 1560 + 1810 + 1380 + 3700 + 6400 \) Now, let's calculate the sum: \( 1500 + 1710 = 3210 \) \( 3210 + 1670 = 4880 \) \( 4880 + 1140 = 6020 \) \( 6020 + 1470 = 7490 \) \( 7490 + 1560 = 9050 \) \( 9050 + 1810 = 10860 \) \( 10860 + 1380 = 12240 \) \( 12240 + 3700 = 15940 \) \( 15940 + 6400 = 22340 \) The sum of all the salaries is \( \$ 22340 \). Next, we divide the sum by the total number of employees (10) to find the mean: \( \text{Mean} = \frac{\text{Sum of salaries}}{\text{Total number of employees}} \) \( \text{Mean} = \frac{22340}{10} \) Now, let's calculate the mean: Calculate the value by following steps: - step0: Calculate: \(\frac{22340}{10}\) - step1: Divide the terms: \(2234\)

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The Deep Dive

To find the mean, you need to add up all the salaries and then divide by the number of employees. So, adding them together gives you \( \$ 1500 + \$ 1710 + \$ 1670 + \$ 1140 + \$ 1470 + \$ 1560 + \$ 1810 + \$ 1380 + \$ 3700 + \$ 6400 = \$ 19540 \). Next, divide by 10 (the number of employees): \( \$ 19540 \div 10 = \$ 1954 \). The mean is \( \$ 1954 \). Now, did you know that salary structures vary widely depending on location, industry, and even the role within a company? The high salary of \( \$ 6400 \) can dramatically skew the mean, highlighting the importance of considering the median for a clearer picture of employee remuneration. It’s a classic case of how averages can sometimes mislead! To avoid common pitfalls in calculating the mean, always remember to double-check your addition and the number of items you're dividing by. It's also wise to review the data set for outliers, as they can really inflate your results, just like that outlier salary of \( \$ 6400 \) in this example!

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