Leonard measured the mass of each pumpkin in his patch in kilograms. He created both a histogram and a box plot to display the same data:

\[0\]\[2\]\[4\]\[6\]\[8\]\[10\]\[0\]\[3\]\[6\]\[9\]\[12\]\[15\]**Mass (kg)Number of pumpkins**

\[0\]\[2\]\[4\]\[6\]\[8\]\[10\]\[12\]\[14\]**Mass (kg)**

**Which display can be used to find the maximum mass?**

Choose 1 answer:

Choose 1 answer:

(Choice A)   

The histogram

A

The histogram

(Choice B)   

The box plot

B

The box plot

**Which display can be used to find that there were \[25\] pumpkins in Leonard's patch?**

Choose 1 answer:

Choose 1 answer:

(Choice A)   

The histogram

A

The histogram

(Choice B)   

The box plot

B

The box plot

Let's analyze the two displays (the histogram and the box plot) to answer the questions:

### 1. **Which display can be used to find the maximum mass?**

- **Histogram:** A histogram shows the distribution of data across different intervals (or bins). It doesn't directly provide the maximum value unless the intervals are very specific. Even then, you would only know that the maximum falls within a particular range, not the exact value.
- **Box Plot:** The box plot typically shows the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. The maximum mass would be indicated by the end of the right whisker.

**Answer:** The box plot can be used to find the maximum mass.  
**Correct Choice:** **B. The box plot**

### 2. **Which display can be used to find that there were 25 pumpkins in Leonard's patch?**

- **Histogram:** A histogram shows the frequency of data within each interval. By summing up the frequencies (the heights of the bars), you can determine the total number of pumpkins.
- **Box Plot:** A box plot does not show individual frequencies, so it doesn't provide information on the total number of data points.

**Answer:** The histogram can be used to find that there were 25 pumpkins in Leonard's patch.  
**Correct Choice:** **A. The histogram**

Would you like more details or have any questions? Here are some related questions:

1. How can you determine the interquartile range (IQR) from a box plot?
2. What additional information can a histogram provide that a box plot cannot?
3. How would you estimate the mean mass using the histogram?
4. Can you determine the range of the data using a histogram?
5. How does the shape of the data distribution appear in both the histogram and the box plot?
6. What would the histogram look like if the data were normally distributed?
7. How can outliers be identified in a box plot?
8. What information would be lost if you only had the box plot and not the histogram?

**Tip:** When analyzing data, use a histogram to understand the distribution and frequency of data within intervals, while a box plot is best for quickly identifying summary statistics like the median, quartiles, and range.

Learn about histograms and box plots through a practical example of analyzing pumpkin mass data. Discover which display is used to find the maximum mass and how to determine the number of pumpkins in a patch using statistical visualizations.

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