Question

1. make a stem-and-leaf plot
2. which representation best shows frequency? why?
3. which representation best shows exact data values? why?
4. in what situation would a histogram be more useful than a line plot or circle graph?
5. how does a histogram compare to a line plot, circle graph, and stem-and-leaf plot when representing the same data?

Explanation:

To answer these questions, we analyze each one based on the characteristics of different data representations (histogram, line plot, circle graph, stem - and - leaf plot):

Question 1

A histogram is the best representation to show frequency. In a histogram, the height of each bar represents the frequency of data within a particular interval. The bars are adjacent to each other, and it is designed to visually display the distribution of data frequencies across different intervals. Line plots show the frequency of individual data points but can be less clear for grouped data. Circle graphs (pie charts) show the proportion of different categories rather than the frequency of data values. Stem - and - leaf plots show the data values and their distribution but are not as straightforward as histograms when it comes to showing the frequency of data in different intervals at a glance.

A stem - and - leaf plot best shows exact data values. In a stem - and - leaf plot, the stem represents the leading digit(s) of the data values, and the leaves represent the trailing digit(s). So, we can directly see the individual data values from the plot. Histograms show data in intervals and do not display the exact data values. Line plots show the frequency of individual data points but can be messy with a large number of data points. Circle graphs show the proportion of categories and not the exact data values.

A histogram is more useful than a line plot or a circle graph when we want to show the frequency distribution of continuous or grouped data. For example, if we have data about the heights of a large group of people (where we group the heights into intervals like 150 - 155 cm, 155 - 160 cm, etc.), a histogram can clearly show how many people fall into each height interval. A line plot is better for showing the frequency of individual data points and can become cluttered with grouped data. A circle graph is used to show the proportion of different categories, not the frequency distribution of grouped numerical data.

Answer:

A histogram best shows frequency. Because the height of each bar in a histogram represents the frequency of data within a specific interval, and it is designed to visually display the distribution of data frequencies across different intervals.

Question 2