Problem 19 - Basic Statistics for Business and Economics

Question

A headline in a Toledo, Ohio, newspaper reported that crime was on the decline. Listed below are the number of homicides from 1986 to \(2003 .\) Draw a line chart to summarize the data and write a brief summary of the homicide rates for the last 18 years. $$ \begin{array}{|ccccc|} \hline \text { Year } & \text { Homicides } & & \text { Year } & \text { Homicides } \\ \hline 1986 & 21 & & 1995 & 35 \\ 1987 & 34 & & 1996 & 30 \\ 1988 & 26 & & 1997 & 28 \\ 1989 & 42 & & 1998 & 25 \\ 1990 & 37 & & 1999 & 21 \\ 1991 & 37 & & 2000 & 19 \\ 1992 & 44 & & 2001 & 23 \\ 1993 & 45 & & 2002 & 27 \\ 1994 & 40 & & 2003 & 23 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The line chart shows fluctuations in homicide rates with a general trend of decline from 1989 to 2003.

Step 1: Organize the Data in Order

First, it's important to have the data clearly organized with consecutive years on the horizontal axis of the graph. Here, the years 1986 to 2003 are arranged alongside their respective homicide counts.

Step 2: Create a Two-Axis Grid for Plotting

Prepare a two-axis grid for the line chart with the year on the x-axis (horizontal) and the number of homicides on the y-axis (vertical). This will help display the data visually.

Step 3: Plot the Data Points for Each Year

For each year from 1986 to 2003, plot a point on the grid according to the corresponding homicide number. For example, for the year 1986, plot a point at 21 on the y-axis.

Step 4: Connect the Data Points with a Line

Once all points have been plotted for each year, connect them with a straight line in chronological order. This line will help illustrate the trend over time.

Step 5: Analyze and Summarize the Chart

Examine the completed line chart to observe the trend in homicide rates over the years. Initially, the chart shows a decline from 1989 to 1990, some fluctuations in the following years, and a general decline towards 2003.

Key Concepts

Line Chart

A line chart is a simple yet powerful tool for data visualization in statistics, particularly useful for displaying changes over time. It consists of a series of data points connected by straight line segments on a two-axis grid.
This visualization helps in understanding patterns or trends in the data.

When creating a line chart, you begin by plotting each data point on a coordinate system where one axis represents the time periods (e.g., years) and the other represents the variable you're interested in, such as the number of homicides in our example.

• The x-axis typically displays the time periods in a sequential manner, making it easy to follow chronological events.
• The y-axis displays the data values you want to analyze.

After plotting the points, you connect them in sequence to reveal how the values change over time, allowing for easy identification of trends or shifts.

Data Analysis

Data analysis is the process of inspecting, cleansing, and modeling raw data with the goal of discovering meaningful information. In the context of our homicide data, it involves examining the plotted points to understand better insights into the overall situation.

In analyzing our line chart:

• First, take note of any clear increases or decreases in the number of homicides over the years.
• Look for patterns, such as periodic peaks or declines.
• Identify any outliers or anomalies that may require further investigation.

This step can lead to more profound insights, such as recognizing potential causes for fluctuations and exploring correlations with other events or conditions. Thorough analysis forms the basis for more informed decision-making.

Trend Analysis

Trend analysis is a specific type of data analysis focusing on the identification of patterns or tendencies over time. By analyzing the trends in our homicide data from 1986 to 2003, we can determine if the headline about declining crime rates holds true.

The completed line chart provides a visual representation, allowing us to observe:

• Periods of increase, such as between 1992 and 1993 when homicides peaked.
• Declines, like the drop from 44 homicides in 1992 to 23 by 2001.
• Overall tendencies, such as the general downward trend in recent years supported by both the chart and numerical data.

Such analysis is essential for drawing conclusions and supporting claims, like the newspaper's report of crime decline, with evidence visible in trends. It helps not only in the criminal field but in any area where longitudinal data is available and actionable insights are required.