https://file.aiquickdraw.com/mathbot/file/1730221561047p2b2rro1.jpg

To analyze this histogram and answer the questions:

### 1. Histogram Shape
The histogram appears roughly symmetric, as the bars are distributed fairly evenly around a central peak. This pattern suggests the distribution is likely **symmetric** rather than skewed.

- **Answer**: Check **symmetric**.

### 2. Appropriate Measure of Center
Since the data distribution is symmetric, the **mean** is typically the preferred measure of center, as it accurately represents the central tendency in symmetric distributions.

- **Answer**: Select **mean**.

### 3. Appropriate Measure of Spread
For symmetric data distributions, the **standard deviation** is generally the best measure of spread, as it considers the average deviation of data points from the mean.

- **Answer**: Select **standard deviation**.

Let me know if you need further explanations on any part.

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### Further Questions to Explore
1. Why is the mean preferred over the median for symmetric distributions?
2. How does the IQR differ from standard deviation in measuring spread?
3. What factors can cause skewness in histograms?
4. How can we interpret data that is bimodal in a histogram?
5. Why is range less informative than standard deviation or IQR?

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**Tip:** In symmetric distributions, mean and median are often close in value, but standard deviation provides a more precise measurement of spread than the range.

The histogram below shows the distances (in meters) of all qualifying throws for the women’s javelin event at the 2004 Summer Olympics. Identify if the histogram is right skewed, left skewed, or symmetric. Then, determine the most appropriate measure of center and measure of spread for this data.

Understand how to analyze the distribution of data in a histogram showing distances of qualifying javelin throws in the 2004 Summer Olympics. This guide covers identifying symmetry in data distribution and choosing appropriate measures of center and spread.

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