8,12,32,10,3,4,4,4,4,5,12,20 Find the mean, median , mode 

To find the **mean**, **median**, and **mode** of the data set:  
\[ 8, 12, 32, 10, 3, 4, 4, 4, 4, 5, 12, 20 \]

### 1. **Mean** (average):
To find the mean, sum up all the numbers, then divide by the total number of values.

\[
\text{Mean} = \frac{8 + 12 + 32 + 10 + 3 + 4 + 4 + 4 + 4 + 5 + 12 + 20}{12}
\]

\[
\text{Mean} = \frac{118}{12} \approx 9.83
\]

### 2. **Median** (middle value):
To find the median, first arrange the numbers in ascending order:

\[ 3, 4, 4, 4, 4, 5, 8, 10, 12, 12, 20, 32 \]

Since there are 12 values (an even number), the median will be the average of the 6th and 7th values. These values are 5 and 8.

\[
\text{Median} = \frac{5 + 8}{2} = \frac{13}{2} = 6.5
\]

### 3. **Mode** (most frequent value):
The mode is the value that appears most often. In this case, 4 appears **four times**.

\[
\text{Mode} = 4
\]

### Summary:
- **Mean**: 9.83  
- **Median**: 6.5  
- **Mode**: 4

Would you like further clarification or details? Here are five questions to explore:

1. How does the mean change if the largest value (32) is removed?
2. What happens to the mode if another number appears four times?
3. Can a data set have more than one mode?
4. Why is the median less sensitive to outliers than the mean?
5. How would adding a very large number affect the mean, median, and mode?

**Tip**: The median is particularly useful for skewed data sets because it isn't influenced by extreme values.

8, 12, 32, 10, 3, 4, 4, 4, 4, 5, 12, 20 Find the mean, median, mode

Learn how to calculate the mean, median, and mode of the data set: 8, 12, 32, 10, 3, 4, 4, 4, 4, 5, 12, 20. This problem involves key statistical concepts and is ideal for students in Grades 6-8.

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