Based on the mean and median calculated above, would you expect this data to be symmetric, skewed to the left or skewed to the right and why?
32, 33, 34, 40, 45, 52, 64, 64, 91, 125

To determine whether the data is symmetric, skewed to the left, or skewed to the right based on the mean and median, let's first calculate both.

### 1. Mean:
The mean is the sum of all the data points divided by the number of data points.

\[
\text{Mean} = \frac{32 + 33 + 34 + 40 + 45 + 52 + 64 + 64 + 91 + 125}{10} = \frac{580}{10} = 58
\]

### 2. Median:
The median is the middle value when the data is ordered. Since we have 10 data points, the median is the average of the 5th and 6th values in the ordered list:

Ordered list: \(32, 33, 34, 40, 45, 52, 64, 64, 91, 125\)

The 5th and 6th values are 45 and 52.

\[
\text{Median} = \frac{45 + 52}{2} = \frac{97}{2} = 48.5
\]

### Interpretation:
- **Mean** = 58
- **Median** = 48.5

Since the **mean** is greater than the **median**, this suggests that the data is **skewed to the right** (positively skewed). This is because the larger values (especially 91 and 125) pull the mean higher, while the median remains closer to the central values of the dataset.

### Conclusion:
The data is **skewed to the right** because the mean is greater than the median, indicating that there are larger values in the dataset that are affecting the mean more than the median.

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Would you like more details on this, or do you have any questions? Here are five related questions to deepen your understanding:

1. How would the data look if it were symmetric instead of skewed?
2. How does the presence of outliers affect the mean and median?
3. What is the difference between positive and negative skewness in data?
4. How could you visualize this data to confirm its skewness?
5. Can data have the same mean and median but still be skewed?

**Tip:** In skewed data, the tail pulls the mean in the direction of the skew, while the median remains relatively unaffected by extreme values.

Based on the mean and median calculated above, would you expect this data to be symmetric, skewed to the left or skewed to the right and why? 32, 33, 34, 40, 45, 52, 64, 64, 91, 125

Explore how to determine whether a dataset is symmetric or skewed based on its mean and median values. This example uses a dataset of 10 numbers, including 32, 33, and 125, and shows how a higher mean compared to the median suggests right skewness. Ideal for Grades 9-12 students learning statistics.

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