Answer the following based on the histograms shown in the next column.
a. Which measure of central tendency would you recommend reporting for the data whose histogram is shown in Figure I? Why? b. Which one has more dispersion? Explain.

Verified step by step guidance

1. Step 1: Examine the shape and spread of the histogram in Figure I. Notice that the data is roughly symmetric and centered around 500, with values ranging from about 200 to 800. This suggests the data is fairly evenly distributed around the center.
2. Step 2: For Figure I, since the distribution appears symmetric without strong skewness or outliers, the mean is a suitable measure of central tendency to report. The mean takes into account all data points and provides a good summary for symmetric distributions.
3. Step 3: Compare the spread (dispersion) of the two histograms. Histogram I covers a wider range of values (approximately 200 to 800), while Histogram II covers a narrower range (approximately 400 to 600). This indicates that Histogram I has more variability in the data.
4. Step 4: To quantify dispersion, consider measures like the range or standard deviation. Since Histogram I has a larger range and the bars are spread out more, it has greater dispersion compared to Histogram II, which is more concentrated around its center.
5. Step 5: Summarize your findings: recommend the mean for Figure I due to its symmetric shape, and state that Figure I has more dispersion because its data values are spread over a wider range compared to Figure II.

Key Concepts

Measures of Central Tendency

Measures of central tendency summarize a data set with a single value representing its center, commonly the mean, median, or mode. The mean is sensitive to extreme values, while the median is more robust in skewed distributions. Choosing the appropriate measure depends on the data's shape and presence of outliers.

Data Dispersion

Dispersion describes the spread or variability of data points in a distribution. Common measures include range, variance, and standard deviation. Greater dispersion indicates data points are more spread out, while lower dispersion means they are clustered closer to the center.

Interpreting Histograms

Histograms graphically display the frequency distribution of data, showing how data values are distributed across intervals. They help identify the shape, central tendency, and spread of the data, which are essential for selecting appropriate statistical measures and understanding data characteristics.