# Histogram And Frequency Polygon In Statistics Pdf

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## Histograms, Frequency Polygons, and Time Series Graphs

For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of values or more. A histogram consists of contiguous adjoining boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents for instance, distance from your home to school.

The vertical axis is labeled either frequency or relative frequency or percent frequency or probability. The graph will have the same shape with either label. The histogram like the stemplot can give you the shape of the data, the center, and the spread of the data. The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample.

Remember, frequency is defined as the number of times an answer occurs. For example, if three students in Mr. To construct a histogram , first decide how many bars or intervals , also called classes, represent the data. Many histograms consist of five to 15 bars or classes for clarity.

The number of bars needs to be chosen. Choose a starting point for the first interval to be less than the smallest data value. A convenient starting point is a lower value carried out to one more decimal place than the value with the most decimal places. For example, if the value with the most decimal places is 6. We say that 6. If the value with the most decimal places is 2. If the value with the most decimal places is 3. If all the data happen to be integers and the smallest value is two, then a convenient starting point is 1.

Also, when the starting point and other boundaries are carried to one additional decimal place, no data value will fall on a boundary. The next two examples go into detail about how to construct a histogram using continuous data and how to create a histogram using discrete data. The following data are the heights in inches to the nearest half inch of male semiprofessional soccer players.

The heights are continuous data, since height is measured. The smallest data value is Since the data with the most decimal places has one decimal for instance, Since the numbers 0. The starting point is, then, 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 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. For example, if there are values of data, take the square root of and round to 12 bars or intervals.

The heights 60 through The heights that are The heights that are 64 through The heights 66 through The heights 68 through The heights 70 through 71 are in the interval The heights 72 through The height 74 is in the interval The following histogram displays the heights on the x -axis and relative frequency on the y -axis.

The following data are the shoe sizes of 50 male students. 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 suggests using 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 0.

Then the starting point is 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. Since the data consist of the numbers 1, 2, 3, 4, 5, 6, and the starting point is 0. The following histogram displays the number of books on the x -axis and the frequency on the y -axis.

Go to [link]. There are calculator instructions for entering data and for creating a customized histogram. Create the histogram for [link]. 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.

Since the data consist of the numbers 1, 2, 3, and the starting point is 0. 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. Count the money bills and change in your pocket or purse. Your instructor will record the amounts. As a class, construct a histogram displaying the data. Discuss how many intervals you think is appropriate. You may want to experiment with the number of intervals. Frequency polygons are analogous to line graphs, and just as line graphs make continuous data visually easy to interpret, so too do frequency polygons. To construct a frequency polygon, first examine the data and decide on the number of intervals, or class intervals, to use on the x -axis and y -axis.

After choosing the appropriate ranges, begin plotting the data points. After all the points are plotted, draw line segments to connect them. The first label on the x -axis is This represents an interval extending from Since the lowest test score is The point labeled This reasoning is followed for each of the remaining intervals with the point Again, this interval contains no data and is only used so that the graph will touch the x -axis.

Looking at the graph, we say that this distribution is skewed because one side of the graph does not mirror the other side. Construct a frequency polygon of U. Since there are no ages less than

## Histograms, Frequency Polygons, and Time Series Graphs

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For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A histogram consists of contiguous adjoining boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is more or less a number line, labeled with what the data represents, for example, distance from your home to school. The vertical axis is labeled either frequency or relative frequency or percent frequency or probability. The graph will have the same shape with either label.

The charts and graphs illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts, and time series graphs. A graph that combines the.

Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 3. Frequency Distributions. Why should I choose AnalystNotes? AnalystNotes specializes in helping candidates pass.

With SPSS for some diagrams there are different options to generate the same output. The two most commonly ones are by using the Chart Builder, or the older Legacy dialogs both under the Graphs menu. Some diagrams can also be made using the Frequencies option the same as used for the tables , some the Explore option, and some by using an already generated frequency table or other diagram.

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5 Response
1. Treasamesis

For most of the work you do in this book, you will use a histogram to display the data.

2. Gimena U.