Problem 18 - Algebra 1: Concepts and Skills

Question

The table shows the population (in thousands) of California following the Gold Rush of 1849. Make a line graph of the data. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Year } & {1850} & {1860} & {1870} & {1880} & {1890} \\ \hline \text { Population } & {93} & {380} & {560} & {865} & {1213} \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The line graph represents the population growth of California from 1850 to 1890. The population figures for each year are plotted against the year on the x-axis, and joined with straight lines.

Step 1: Identify the Data

The data provided is a set of years (1850, 1860, 1870, 1880, 1890) and their corresponding population figures (93, 380, 560, 865, 1213). Each year's population is given in thousands.

Step 2: Prepare the Graph

Draw a line graph with two axes. The horizontal axis (x-axis) will represent the years and the vertical axis (y-axis) will represent the population in thousands.

Step 3: Label the Axes

Label the x-axis as 'Year' and the y-axis as 'Population in Thousands'. Make sure the scales are appropriate for the range of data that needs to be plotted. For the x-axis, the range should be from 1850 to 1890, and for the y-axis the range should be from 0 to 1300 (to incorporate the highest population figure of 1213).

Step 4: Plot the Data

Plot each year against its corresponding population on the graph. Each year's population determines the point's height above the x-axis. For example, the point for the year 1850 will be plotted above 1850 on the x-axis at a height corresponding to 93 on the y-axis.

Step 5: Draw the Line

Join the plotted points with straight lines. This will create a line graph showing the population growth of California from 1850 to 1890.

Key Concepts

Population Data

Population data provides critical insights into how the number of people in a particular area changes over time. In this exercise, we're given population figures of California in thousands for different years, following the Gold Rush of 1849. Gathering data like this helps us understand trends and demographic changes.

For example, when looking at the years 1850 (93,000 people) to 1890 (1,213,000 people), there is a noticeable increase in population. This gives us a clue about historical events or trends that might have influenced such growth.

• Rapid population increase often indicates economic opportunities, like those brought by the Gold Rush.
• Population data is usually organized in tables to aid ease of interpretation and analysis.
• When analyzed, it can guide policy-making, urban planning, and provide historical insights.

Data points like these serve as the foundation for creating effective visual representations such as graphs, which can then allow for even easier analysis and interpretation.

Graphing Techniques

Graphing techniques are essential for visualizing data effectively. In this case, we're using a line graph to represent population data over time. Line graphs are particularly useful when you are interested in how a variable changes at regular intervals.

• The horizontal axis (x-axis) should represent the independent variable, which is typically time, and the vertical axis (y-axis) should represent the dependent variable, which is the population in this case.
• Labeling is crucial: ensure that each axis is clearly marked with the units of measure, such as "Population in Thousands" and "Years."
• Choose an appropriate scale for each axis. This ensures all data points fit nicely on the graph and are easy to read.

Once the graph is set up, you plot the points by determining the coordinates (year, population). Each plot represents a point in history reflected in the population data. Finally, drawing straight lines between the points helps visualize trends clearly. Graphs condense large amounts of data into an easily interpretable form.

Historical Data Analysis

Analyzing historical data involves examining data from past events to understand trends and impacts over time. The population figures provided for California during the 19th century reflect significant historical developments coinciding with the Gold Rush era. This analysis enables us to make several interpretations:

California's population increased substantially after the Gold Rush. This suggests a major influx of settlers seeking opportunities. By comparing population data to historical events, one can identify cause-and-effect relationships and understand broader societal changes.

• Historical data analysis provides context—how and why things happened in the past.
• This context aids in predicting future trends by learning from historical patterns.
• It also helps us appreciate the dynamic nature of human demographics and its interaction with historical events.

Applying such analyses helps educators, historians, and policymakers learn from the past to better navigate the future. With well-analyzed historical data, society gains a better understanding of its cumulative history, informing decisions ranging from education to economics.