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which of the distributions is likely to have the largest mean

Looking at the histograms, the mean of a distribution is closely related to the position of the "center" of the distribution, especially when it is skewed. In this case, we can analyze the histograms visually to assess which one might have the largest mean.

- **A (Red)**: Symmetrical, but the distribution is centered around 1. The mean is likely around 1.
- **B (Green)**: Symmetrical, with data roughly centered around 1. The mean is likely around 1.
- **C (Blue)**: Symmetrical, with data centered around 50, so the mean is around 50.
- **D (Gray)**: Slight right skew, with a center around 15. The mean will likely be slightly above the center, closer to 15 or more.
- **E (Black)**: Symmetrical, with a mean centered at 0.
- **F (Teal)**: Slight right skew, with data spread from 0 to 14 and the center around 5. The mean will be above 5, perhaps close to 6.
- **G (White)**: Symmetrical with a mean around 5.
- **H (Yellow)**: Right skew, with most data on the left side. The center is around -1 or 0, and the mean will be slightly greater than the center, but still negative or close to 0.

### Conclusion:
Among these, **Distribution C** (Blue) has the largest mean because it is centered around 50, much higher than the other distributions, which are centered around much smaller values.

Would you like a more detailed explanation or comparison of any specific distributions? Here are 5 follow-up questions you might consider:

1. What is the effect of skewness on the mean of a distribution?
2. How does symmetry affect the mean and median relationship in distributions like B or E?
3. What can we infer about the standard deviation from these histograms?
4. Can we estimate the median and compare it with the mean for these distributions?
5. How would outliers affect the mean in a skewed distribution like F or H?

**Tip:** In a skewed distribution, the mean tends to be pulled towards the longer tail (right or left), while the median remains closer to the central value.

Which of the distributions is likely to have the largest mean?

Analyze various histograms to determine which distribution likely has the largest mean. This question involves core concepts of descriptive statistics, such as the mean and skewness of distributions, and is suitable for students in Grades 9-12. Visual interpretation of distributions is a key skill for understanding how data is spread and centered.

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