Use the relative frequency histogram to describe any patterns with the data.

Verified step by step guidance

1. Observe the relative frequency histogram provided. The x-axis represents the response times in minutes, while the y-axis represents the relative frequency as a percentage.
2. Identify the range of response times. The histogram shows data grouped into intervals: 10.5-11.5, 11.5-12.5, 12.5-13.5, and 13.5-14.5 minutes.
3. Note the height of the bars, which indicates the relative frequency for each interval. The tallest bars correspond to the intervals 11.5-12.5 minutes, showing the highest relative frequency (approximately 40%).
4. Describe the pattern: The data suggests that most campus security response times fall within the 11.5-12.5 minute range, with fewer responses occurring in the intervals 10.5-11.5 and 13.5-14.5 minutes.
5. Conclude that the distribution of response times is unimodal and slightly skewed to the right, as the frequency decreases for higher intervals beyond 12.5 minutes.

Key Concepts

Relative Frequency

Relative frequency is the ratio of the frequency of a particular category to the total number of observations. It is expressed as a percentage and helps in understanding the proportion of data points that fall within specific intervals. In the context of the histogram, it indicates how often response times occur relative to the total response times recorded.

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (bins) and the frequency of data points within each interval is represented by the height of bars. In this case, the histogram displays campus security response times, allowing for visual analysis of patterns such as central tendency and variability in response times.

Patterns in Data

Identifying patterns in data involves analyzing the distribution and trends within the dataset. In the histogram, patterns may include peaks (modes), gaps, or trends that indicate how response times are clustered. For instance, a higher relative frequency in certain time intervals suggests that those response times are more common, which can inform operational decisions for campus security.