Information About Auto Theft Rates And Numbers

Some Information About Auto Theft Rates Number Of Auto Thefts Per 100

Some information about auto theft rates (number of auto thefts per 100,000 population) for a sample of 178 cities in two different years is summarized below. Express the statistical information in words. What changes were there in the overall shape of the distribution of this variable? In central tendency? In dispersion?

Mean 150.32 125.17 Median 117.17 123.01 Standard Deviation 12.23 7.

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The data provided compares auto theft rates in two different years across a sample of 178 cities, offering insights into how this criminal activity has evolved over time. The primary statistical measures include the mean, median, and standard deviation for each year, reflecting aspects of central tendency and dispersion, respectively. In the first year, the mean auto theft rate was 150.32 per 100,000 population, with a median of 117.17, and an associated standard deviation of 12.23. In the subsequent year, these values shifted to a mean of 125.17 and a median of 123.01, with a decreased standard deviation of 7, indicating notable changes in the distribution characteristics.

Analyzing the overall shape of the distribution, the reduction in both mean and standard deviation suggests a decrease in the variability and spread of auto theft rates among the cities. The decline in the mean indicates an overall reduction in auto thefts per 100,000 population, which could reflect improved law enforcement, community initiatives, or other socioeconomic factors affecting crime rates. The change in the median, from 117.17 to 123.01, indicates a slight shift in the distribution's center, moving closer to the mean, which might suggest a narrowing in the range of theft rates or a redistribution of the rates among different cities.

From a shape perspective, if one visualizes the distribution, the decreased standard deviation hints at a more concentrated distribution around the central tendency in the second year, implying fewer cities experiencing extremely high or low auto theft rates. This contraction signifies a potential stabilization in auto theft activity across the sampled census of cities. Regarding central tendency, both the mean and median changed in a manner suggestive of overall improvement—namely, a decrease in theft rates—yet the median in the second year actually increased slightly, suggesting that the middle value faced less variation and perhaps that the distribution became more symmetric and less skewed.

Dispersion, represented by the standard deviation, decreased substantially from 12.23 to 7, further supporting the conclusion that the variation among cities' auto theft rates diminished over time. This reduction implies a more uniform distribution with fewer cities experiencing markedly higher or lower theft rates, contributing to an overall trend of stabilization and potential improvement in crime control measures.

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