How is frequency polygon plotted

A frequency polygon for psychology test scores shown in Figure 1 was constructed from the frequency table shown in Table 1. The first label on the X-axis is This represents an interval extending from Since the lowest test score is 46, this interval has a frequency of 0.

The point labeled 45 represents the interval from There are three scores in this interval. There are scores in the interval that surrounds You can easily discern the shape of the distribution from Figure 1.

Most of the scores are between 65 and It is clear that the distribution is not symmetric inasmuch as good scores to the right trail off more gradually than poor scores to the left.

In the terminology of Chapter 3 where we will study shapes of distributions more systematically , the distribution is skewed. Figure 1. Frequency polygon for the psychology test scores. A cumulative frequency polygon for the same test scores is shown in Figure 2.

The graph is the same as before except that the Y value for each point is the number of students in the corresponding class interval plus all numbers in lower intervals.

For example, there are no scores in the interval labeled "35," three in the interval "45," and 10 in the interval " Since students took the test, the cumulative frequency for the last interval is Figure 2. Cumulative frequency polygon for the psychology test scores. Frequency polygons are useful for comparing distributions. This is achieved by overlaying the frequency polygons drawn for different data sets. Figure 3 provides an example.

The data come from a task in which the goal is to move a computer cursor to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial. The two distributions one for each target are plotted together in Figure 3. Since the numbers [latex]0. The starting point is, then, [latex] Next, calculate the width of each bar or class interval.

To calculate this width, subtract the starting point from the ending value and divide by the number of bars you must choose the number of bars you desire. Suppose you choose eight bars. We will round up to two and make each bar or class interval two units wide. Rounding up to two is one way to prevent a value from falling on a boundary. Rounding to the next number is often necessary even if it goes against the standard rules of rounding.

For this example, using [latex]1. A guideline that is followed by some for the width of a bar or class interval is to take the square root of the number of data values and then round to the nearest whole number, if necessary.

The heights that are [latex] The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars. The calculations suggest using [latex]0. You can also use an interval with a width equal to one.

The following data are the number of books bought by 50 part-time college students at ABC College. The number of books is discrete data , since books are counted. Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books. Because the data are integers, subtract [latex]0. Then the starting point is [latex]0. If the data are discrete and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient.

The following data are the number of sports played by 50 student athletes. The number of sports is discrete data since sports are counted. Eight student athletes play three sports.

Fill in the blanks for the following sentence. Some values in this data set fall on boundaries for the class intervals. A value is counted in a class interval if it falls on the left boundary, but not if it falls on the right boundary. Different researchers may set up histograms for the same data in different ways. There is more than one correct way to set up a histogram. The following data represent the number of employees at various restaurants in New York City. Using this data, create a histogram.

Frequency polygons are useful for comparing distributions. This is achieved by overlaying the frequency polygons drawn for different data sets. Suppose that we want to study the temperature range of a region for an entire month. Every day at noon we note the temperature and write this down in a log. A variety of statistical studies could be done with this data. We could find the mean or the median temperature for the month.

We could construct a histogram displaying the number of days that temperatures reach a certain range of values. However, all of these methods ignore a portion of the data that we have collected. One feature of the data that we may want to consider is that of time. We can instead use the times given to impose a chronological order on the data.

A graph that recognizes this ordering and displays the changing temperature as the month progresses is called a time series graph. To construct a time series graph, we must look at both pieces of our paired data set. We start with a standard Cartesian coordinate system. The horizontal axis is used to plot the date or time increments, and the vertical axis is used to plot the values of the variable that we are measuring.

By doing this, we make each point on the graph correspond to a date and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur.

Time series graphs are important tools in various applications of statistics.