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.

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?

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.