91Ó°ÊÓ

Refer to Table \(15-13,\) which gives the home-to-school distance \(d\) (rounded to the nearest half-mile) for each of the 27 kindergarten students at Cleansburg Elementary School. $$ \begin{array}{c|c|c|c} \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} & \begin{array}{c} \text { Student } \\ \text { ID } \end{array} & \boldsymbol{d} \\ \hline 1362 & 1.5 & 3921 & 5.0 \\ \hline 1486 & 2.0 & 4355 & 1.0 \\ \hline 1587 & 1.0 & 4454 & 1.5 \\ \hline 1877 & 0.0 & 4561 & 1.5 \\ \hline 1932 & 1.5 & 5482 & 2.5 \\ \hline 1946 & 0.0 & 5533 & 1.5 \\ \hline 2103 & 2.5 & 5717 & 8.5 \\ \hline 2877 & 1.0 & 6307 & 1.5 \\ \hline 2964 & 0.5 & 6573 & 0.5 \\ \hline 3491 & 0.0 & 8436 & 3.0 \\ \hline 3588 & 0.5 & 8592 & 0.0 \\ \hline 3711 & 1.5 & 8964 & 2.0 \\ \hline 3780 & 2.0 & 9205 & 0.5 \\ \hline & & 9658 & 6.0 \\ \hline \end{array} $$ (a) Make a frequency table for the distances in Table \(15-13 .\) (b) Draw a line graph for the data in Table \(15-13\).

Step by step solution

01

Create a frequency table

A frequency table is an organized display of how often each number appears in the set of data. You need to create a table with two columns. In the first column, list all the unique distances that appear in the original table (from 0 to 8.5 miles). In the second column, list the number of students who live at each respective distance from the school. Count the number of students for each distance in the original table and make a note of it in the corresponding cell of the second column of the frequency table.

02

Draw a line graph

The line graph can visualize this data from the frequency table. Each unique distance will form a vertical line or 'bar', with a length proportional to its frequency. On the x-axis, set up the scale and label it as 'Distance (miles)'. On the y-axis, set up a scale for the number of students and label it as 'Number of Students'. Plot the points that correspond to each distance and number from the frequency table and connect them with a line. Keep in mind that each value from the frequency table is represented on the line graph. The order of x-values should be in ascending distance order, from left to right.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency Table

Creating a frequency table is a crucial step in organizing data and making it understandable. In the case of student distances to school, it allows us to see how many students live at each specified distance. You accomplish this by listing each unique distance and counting how often it appears in your data set.

When you construct the table:

• Start by listing every unique distance in a separate column. For instance, a student might live 0, 0.5, 1.0 miles, and so on, up to 8.5 miles.
• Create another column next to it to record the frequency—how often that distance occurs in your dataset.

A frequency table can quickly show you the most common distances. For example, if you see that the distance 1.5 miles appears most frequently, it tells you many students share this proximity to school. Such a table not only condenses a dataset but highlights patterns that can be further analyzed for trends or insights.

Use this approach in various educational settings to better understand patterns, such as attendance versus distance, which can inform planning and resource allocation.

Line Graph

A line graph is a compelling way to visualize the data from a frequency table. It helps to transform numbers into a visual story that is easier to interpret at a glance. While creating one to represent student distances to school:

• Use the horizontal axis (x-axis) to display the distances (e.g., from 0 to 8.5 miles).
• On the vertical axis (y-axis), represent the frequency, i.e., the number of students that live at each distance.

Start by plotting each point where the distance meets its frequency. For example, if three students live 0.5 miles away, and five live 1.0 miles away, you will plot these points on the graph accordingly and connect them with lines.

This line connection operation shows trends over distances visually, making it easy to detect increases or decreases in student numbers with regard to their home distances. A line graph not only facilitates easy pattern recognition but also aids instructors and school authorities in understanding demographic distributions.

Statistical Methods in Education

Statistical methods are invaluable in the field of education, offering a systematic approach to collecting, analyzing, and interpreting data to draw meaningful conclusions. Techniques like frequency tables and line graphs are foundational tools in data analysis.

Educational statistics might cover:

• Analyzing student performance data to identify areas needing improvement.
• Examining enrollment patterns to help with resource planning.
• Studying distance versus educational outcomes as part of school zoning policies.

In our example, utilizing these statistical methods helps translate raw data about distances into s