Short Answer 
To connect a histogram with the mean and median, start by determining the skewness of the histogram, which indicates relationships between the mean and median. Next, evaluate their specific values; the mean’s position relative to the median confirms the skewness and finally conclude the data distribution, with the mean likely being close to the median if the histogram is symmetric.
Step 1: Identifying Histogram Skewness
The first step is to analyze the skewness of the histogram. This involves determining if the histogram is skewed left, skewed right, or symmetric. This classification is important because it helps predict the relationship between the mean and the median:
- Skewed Right: The mean is greater than the median.
- Symmetric: The mean and median are approximately equal.
- Skewed Left: The mean is less than the median.
Step 2: Evaluating Mean and Median Relationships
In the next step, evaluate the specific values of the mean and median from your data set. For instance, if you’ve identified that the median is 29.5, you can then analyze the position of the mean relative to it. Knowing their relationship allows you to confirm the skewness of the histogram:
- If mean > median: Indicates a right skew.
- If mean ‚Äöaa median: Indicates a symmetric shape.
- If mean < median: Indicates a left skew.
Step 3: Conclusion on Data Distribution
The final step is to conclude about the data distribution based on the interpolation from the mean and median analysis. Since the median is 29.5 and the distribution is close to symmetric, we can deduce that:
- The mean will be close to 29.5 as well.
- The histogram shape will resemble a bell curve centered around those values.
- The data set most likely has a distribution similar to that shown in the attached figure.