Questions: 20,30,40,50,50,55,55,55,65,80 (a) Determine the mean, median, and mode for salary. The mean salary is 50 thousand dollars. The median salary is 52.5 thousand dollars. Select the correct choice below and fill in any answer boxes in your choice. A. The mode salary is 55 thousand dollars B. There is no mode.

20,30,40,50,50,55,55,55,65,80 (a) Determine the mean, median, and mode for salary. The mean salary is 50 thousand dollars. The median salary is 52.5 thousand dollars. Select the correct choice below and fill in any answer boxes in your choice. A. The mode salary is 55 thousand dollars B. There is no mode.
Transcript text: $20,30,40,50,50,55,55,55,65,80$ (a) Determine the mean, median, and mode for salary. The mean salary is 50 thousand dollars. (Type an integer or a decimal.) The median salary is 52.5 thousand dollars. (Type an integer or a decimal.) Select the correct choice below and fill in any answer boxes in your choice. A. The mode salary is 55 thousand dollars (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is no mode.
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Solution

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Solution Steps

To determine the mean, median, and mode for the given salary data set, we can follow these steps:

  1. Mean: Calculate the sum of all salaries and divide by the number of salaries.
  2. Median: Sort the data set and find the middle value. If the number of data points is even, the median is the average of the two middle numbers.
  3. Mode: Identify the number that appears most frequently in the data set.
Step 1: Calculate the Mean

The mean salary is calculated by summing all the salaries and dividing by the number of salaries: \[ \text{Mean} = \frac{20 + 30 + 40 + 50 + 50 + 55 + 55 + 55 + 65 + 80}{10} = 50 \]

Step 2: Calculate the Median

To find the median, we first sort the data set and then find the middle value. Since there are 10 data points (an even number), the median is the average of the 5th and 6th values: \[ \text{Median} = \frac{50 + 55}{2} = 52.5 \]

Step 3: Calculate the Mode

The mode is the value that appears most frequently in the data set. Here, the value 55 appears three times, which is more frequent than any other value: \[ \text{Mode} = 55 \]

Final Answer

\[ \boxed{\text{Mean} = 50} \] \[ \boxed{\text{Median} = 52.5} \] \[ \boxed{\text{Mode} = 55} \]

The correct choice for the mode is: \[ \boxed{\text{A. The mode salary is 55 thousand dollars}} \]

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