Calculate the arithmetic mean, median, and mode for the following dataset: [10, 20, 20, 
30, 40, 50].

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

---

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!

Calculate the arithmetic mean, median, and mode for the following dataset: [10, 20, 20, 30, 40, 50].

Learn how to calculate the arithmetic mean, median, and mode for a dataset with values [10, 20, 20, 30, 40, 50]. This solution includes step-by-step instructions for finding each statistic and a detailed explanation of the formulas involved. Suitable for students in Grades 6-8.

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