Question

Using the classmate's frequency distribution below, construct a histogram (for continuous variables) or bar chart (for discrete variables). State two unique observations that can be made based on the data

Answer 1

To construct a histogram, first organize data into equal intervals, count frequencies, draw axes, and scale them. Then use bars of equal width to represent the frequency of each interval. Observations from the histogram can help in understanding data distribution and making decisions like optimal capacity for a new community college.

Step-by-step explanation:

To construct a histogram, you need to organize the classmate's frequency distribution data into equally spaced intervals. Here's how you can do it:

1. Organize your data into a chart with two columns titled Enrollment and Frequency. Choose five to six intervals that cover the range of your data.
2. Once you have your intervals, count the number of data points (instances) that fall into each interval. This will be the frequency for that interval.
3. On graph paper, draw two axes perpendicular to each other. The horizontal axis (x-axis) will represent the intervals of the enrollment data, and the vertical axis (y-axis) will represent the frequency of those intervals.
4. Using a ruler and pencil, draw bars for each interval with heights corresponding to the frequencies. Ensure that the bars are of equal width and are adjacent to each other with no gaps in between for a histogram, as it represents continuous data.
5. Properly scale the axes to accommodate all your data points and frequencies.

After completing the histogram, one might make observations based on the shape and distribution of the data, such as identifying the mode or determining whether the distribution is symmetric or skewed. When choosing between the mean or mode in building a new community college, the mode could be more useful because it shows the most common enrollment size. This could suggest the optimal capacity planning for a new institution, while the mean might be skewed by particularly small or large enrollments.

Regarding the differences between histograms for different data (such as Publisher A, B, and C), it is important to recognize that the choice of bin width and starting point can significantly affect the appearance of a histogram. For discrete data such as the color of cars, a bar chart would be more appropriate than a histogram.