Problem 21 - Basic Statistics for Business and Economics

Question

The following table shows the population, in millions, of the United States in 5 -year intervals from 1950 to \(2000 .\) Develop a line chart depicting the population growth and write a brief report summarizing your findings. $$ \begin{array}{|ccccc|} \hline \text { Year } & \begin{array}{c} \text { Population } \\ \text { (millions) } \end{array} & \text { Year } & \begin{array}{c} \text { Population } \\ \text { (millions) } \end{array} \\ \hline 1950 & 152.3 & 1980 & 227.7 \\ 1955 & 165.9 & 1985 & 238.5 \\ 1960 & 180.7 & 1990 & 249.9 \\ 1965 & 194.3 & 1995 & 263.0 \\ 1970 & 205.1 & 2000 & 281.4 \\ 1975 & 216.0 & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The line chart shows a steady population increase from 1950 to 2000.

Step 1: Organize the Data

We have population data for the years 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, and 2000. The data pairs are: (1950, 152.3), (1955, 165.9), (1960, 180.7), (1965, 194.3), (1970, 205.1), (1975, 216.0), (1980, 227.7), (1985, 238.5), (1990, 249.9), (1995, 263.0), and (2000, 281.4). These values need to be plotted to show population growth.

Step 2: Set up the Axes for the Line Chart

The horizontal axis (x-axis) will represent the years, ranging from 1950 to 2000. The vertical axis (y-axis) will represent the population in millions, ranging from the minimum value 152.3 million to the maximum 281.4 million. Mark each year at 5-year intervals and adjust the population marks to accommodate all values comfortably.

Step 3: Plot the Data Points

For each year listed, place a point on the chart corresponding to its population value. For example, plot a point at (1950, 152.3), another at (1955, 165.9), and so on, until all years and populations have been plotted.

Step 4: Connect the Data Points

Draw lines between successive data points to form the line chart. This will visually connect the population growth over time.

Step 5: Analyze the Chart

Observe the nature of the line chart. Consider the slopes of the lines between the points, as steeper slopes indicate faster growth. Note any trends, such as periods of rapid growth or slowing population increase.

Step 6: Write a Summary Report

Summarize the findings from the line chart. For example, it shows a steady increase in the population of the United States from 1950 to 2000. Highlight any specific trends or interesting points, such as a particularly steep increase in a specific decade.

Key Concepts

Population Growth

Population growth is an important concept that helps us understand how the number of people in a given area changes over time. In the provided data, we are looking at the population of the United States from 1950 to 2000 in 5-year intervals. During these 50 years, the population increased steadily from 152.3 million to 281.4 million. This growth can be influenced by several factors, which include:

• Natural Increase: More births than deaths contribute to population growth.
• Immigration: An increase in people moving to the United States can cause the population to grow.
• Economic Factors: Better job opportunities might attract more people to live in certain areas.

Understanding population growth helps us make predictions about future needs for resources like food, housing, and education. It also assists governments in planning for infrastructure and services to support the growing population. Overall, the consistent increase shown in our dataset indicates a positive trend that governments and policymakers need to consider for sustainable development.

Line Chart

Using a line chart is a powerful way to visually represent data over a period of time. In our exercise, we've used a line chart to depict the population growth of the United States from 1950 to 2000.

Let's break down how to create this line chart:

• Firstly, the x-axis represents years ranging from 1950 to 2000.
• The y-axis shows the population in millions, starting at 152.3 million in 1950 and ending at 281.4 million in 2000.
• Each data point is plotted on the graph based on its year and population value.
• By connecting these points with lines, we can see the trend over the 50-year span.

Line charts are particularly helpful because they allow us to quickly identify patterns and trends. In this chart, we can clearly see the continuous rise in population every five years. Areas where the line steepens indicate periods of faster growth, whereas flatter slopes suggest slower growth periods. With a line chart, one can easily summarize vast amounts of data in a visually accessible format, making complex trends more understandable at a glance.

Statistical Analysis

Statistical analysis involves examining and interpreting data to uncover patterns and insights. In the context of our population data, statistical analysis begins with observing the line chart and quantifying the changes over time.

Key points of focus during statistical analysis include:

• Rate of Growth: Calculating how fast the population grew over each interval. You can find the rate by subtracting the population of the earlier year from the later year for each interval and then dividing by the number of years (here, usually 5).
• Trend Identification: Spot trends in increase—was the growth consistent, or did it spike in certain decades?
• Average Growth: Compute the average growth rate over the entire period by summing up all the growth in each interval and dividing it by the total number of intervals.

With this analysis, we observe that the U.S. population increased by approximately 129.1 million over the 50 years, averaging around 25.82 million every decade. The insights gained from statistical analysis are vital for forecasting future population trends and making informed decisions in policy-making and planning. Overall, it equips analysts and policymakers with the evidence required to address imminent challenges associated with growing populations.