Let's calculate the arithmetic mean, median, and mode for the dataset:

$\{ 10, 20, 20, 30, 40, 50 \}$

1. Arithmetic Mean

The arithmetic mean (average) is the sum of all the values in the dataset divided by the number of values.

$\text{Mean} = \frac{10 + 20 + 20 + 30 + 40 + 50}{6} = \frac{170}{6} \approx 28.33$

So, the mean is approximately 28.33.

2. Median

The median is the middle value of the dataset when it is arranged in ascending order. Since the dataset already appears in ascending order:

$\{ 10, 20, 20, 30, 40, 50 \}$

There are 6 values (an even number), so the median is the average of the 3rd and 4th values.

$\text{Median} = \frac{20 + 30}{2} = \frac{50}{2} = 25$

So, the median is 25.

3. Mode

The mode is the value that appears most frequently in the dataset. In this case, the number 20 appears twice, while all other numbers appear once.

So, the mode is 20.

Summary:

• Mean: 28.33
• Median: 25
• Mode: 20

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Would you like more details on any of the calculations? Or do you have another question?

Related Questions:

1. How does the number of data points affect the median calculation?
2. What happens when there are multiple modes in a dataset?
3. How do you calculate the weighted mean for a given dataset?
4. How would the mean and median change if we added another value to the dataset?
5. What is the difference between the mean and the median in a skewed distribution?

Tip: When calculating the mean, it's important to ensure that all values are included and accurately summed. Double-checking for any missing values can prevent errors!