Assume that the following histograms are drawn on the same scale.
 
 
Which one of the histograms has a mean that is smaller than the median?

Group of answer choices

Histogram III

Histogram I

Histogram IV

Histogram II

To determine which histogram has a mean that is smaller than the median, we need to understand the relationship between the shape of the distribution and the mean and median.

- **Symmetrical Distribution:** The mean and median are equal.
- **Left-Skewed (Negatively Skewed) Distribution:** The mean is less than the median.
- **Right-Skewed (Positively Skewed) Distribution:** The mean is greater than the median.

Given this information:

- **Histogram I**: If Histogram I is left-skewed, the mean will be smaller than the median.
- **Histogram II**: If Histogram II is right-skewed, the mean will be larger than the median.
- **Histogram III**: If Histogram III is symmetrical, the mean and median will be the same.
- **Histogram IV**: If Histogram IV is right-skewed, the mean will be larger than the median.

### Conclusion:
- **Histogram I** (assuming it is left-skewed) is the one where the mean is smaller than the median.

**Answer:** **Histogram I**

### Would you like more details or have any questions?

Here are some related questions:
1. What are the characteristics of left-skewed and right-skewed distributions?
2. How does the shape of a histogram affect the mean and median?
3. Can you explain how to identify the skewness of a distribution by looking at a histogram?
4. What is the relationship between mean, median, and mode in different types of distributions?
5. How can outliers impact the mean and median in a distribution?

**Tip:** When analyzing a histogram, remember that a left-skewed distribution generally has a mean that is less than the median.

Understand which histogram has a mean smaller than the median with a clear analysis of distribution shapes. Learn about left-skewed, right-skewed, and symmetrical distributions in statistics.

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