Problem 18 - Algebra 1

Question

The table shows the number of commercial television stations for different years. Make a line graph of the data. Discuss what the line graph shows. $$\begin{array}{|l|c|c|c|c|c|c|}\hline \text { Year } & 1991 & 1992 & 1993 & 1994 & 1995 & 1996 \\ \hline \text { Number of stations } & 1098 & 1118 & 1137 & 1145 & 1161 & 1174 \\ \hline\end{array}$$

Step-by-Step Solution

Answer

The line graph shows an increasing trend in the number of commercial television stations from 1991 to 1996.

Step 1: Understand the Data

First, review the data set. We have two columns: Year (from 1991 to 1996) and corresponding Number of Stations, showing an incremental trend.

Step 2: Plot the Data on a Graph

Plot the Year on the horizontal (X) axis and the Number of Stations on the vertical (Y) axis. Insert the data points on the graph paper according to the data in the table, then connect these points with a line. Make sure the line starts from the first data point (1991, 1098) and ends at the last data point (1996, 1174)

Step 3: Interpret the Graph

With the completed line graph, we can interpret the trend of the data. The line graph shows an upward trend, which indicates that the number of commercial television stations gradually increased from 1991 to 1996.

Key Concepts

Data Interpretation

When looking at a line graph, the first step is to interpret the data it presents. This graph is a visual representation of how the number of commercial television stations changed over a period of time, specifically from 1991 to 1996. By plotting the data points from the table onto a graph, you can easily identify patterns and trends.

A line graph helps in summarizing complex data into something more understandable. Each data point represents a specific year's station count. The horizontal axis (X-axis) hosts the years, while the vertical axis (Y-axis) depicts the number of stations. Once you connect the points, the overall trend emerges clearly.

The graph for this data set shows an increasing line, which tells us that there was a consistent upward trend in the number of television stations over the years. This interpretation provides a visual overview of the steady growth of commercial television outlets during this time frame.

Trend Analysis

Trend analysis is an important aspect of data interpretation, especially when working with a line graph. In this context, the trend refers to the direction in which the sequence of data is headed. In the case of the commercial television stations from 1991 to 1996, the trend is upward.

Analyzing this trend involves examining the slope of the line graph. A positive slope, such as seen in this example, indicates growth or an increase in the number of stations over the years. Here's what you might consider during trend analysis:

• The steepness of the line: A steeper line suggests faster growth.
• The consistency: A smooth, uninterrupted line points to steady growth over time.
• The particular years with the highest growth: By comparing the differences between consecutive years, you can pinpoint when growth was most significant.

By conducting a thorough trend analysis, you can provide a more comprehensive understanding of how the number of stations evolved, along with insights into the media industry's expansion during the 1990s.

Graph Plotting

Graph plotting is the process of translating data points onto a coordinate system, which in the case of a line graph, involves setting markers on the respective axes and then connecting them with lines. Here’s how to achieve accurate graph plotting and make your graph as informative as possible.

Start by determining the appropriate scale for both axes. For the given data involving years and station numbers, find intervals that fit well with your paper or graphing tool. Typically, the years are marked on the X-axis, while the number of stations ascends on the Y-axis.

Once the scales are set, plot each point by matching the year with its corresponding number of stations using their respective coordinates. In our exercise, these years ranged from 1991 to 1996, with associated station numbers from 1098 in 1991 to 1174 in 1996.

• Check your scale carefully to ensure precision.
• Plot points accurately to avoid distortion.
• Once all points are set, connect them with a straight line.
• Add labels and a title for clarity.

Attention to detail in plotting can significantly impact the graph's readability and accuracy, aiding in better data interpretation and trend analysis later on.