Frequency diagrams and their various type

A data set can be simple, complex, and large in number. Therefore it becomes significant to classify them in a compact form that is easy to read, comprehend and analyze. Generally, data can be presented in three forms:

• Textual representation, 
• Tabular representation, and
• Diagrammatic representation.

Frequency diagrams are a diagrammatic or graphical representation of data, enabling a quick and clear understanding of complex data sets. Frequency diagrams are created to avoid mistakes and provide a bird’s eye view of large data sets. The large data sets are first grouped under various frequencies and then diagrammatically represented on a paper. Besides giving an accurate picture of data, the frequency diagrams reflect a definite pattern. 

The advantages of frequency diagrams are:

• It simplifies complex data sets.
• Helps represent data using appropriate diagrams.
• Saves time.
• Makes data more meaningful.
• Helps in planning, extrapolating, interpolating, and decision making with the given data.

Types of Frequency Diagrams 

After being sorted efficiently, the data sets are arranged into a frequency table, then graphically represented in one of the types of frequency diagrams. The various types of frequency diagrams can be classified into five classes – Histogram, frequency polygon, frequency curve, ogive, and arithmetic line graph.

• Histogram- A histogram is a graphical representation of a frequency distribution of a continuous series. It is a two-dimensional diagram that looks like a bar chart. However, the two are very much different, although they look identical. While there is no space between two rectangles or bars in a histogram, a bar diagram has space between two consecutive bars showing frequencies of two different class intervals. Usually, the class intervals in a histogram are unequal but continuous. Discontinuous class intervals are always converted into continuous series before making a histogram.

To create a histogram, the frequencies are first divided into class intervals. The next important thing is to ascertain the frequency density under various class intervals. The area of the bars in a histogram represents the frequency. To calculate the height of the bar, the frequencies are divided by class width (the difference between the upper and lower limits of a class).

• Frequency Polygon – A frequency polygon is a plane bounded by straight lines. Usually, four or more lines are used to create a frequency polygon. A frequency polygon can easily be created by joining the midpoints of the top of all bars or consecutive rectangles of the histogram with small straight lines. The two ends are joined using a dotted line at the baseline to derive the area under the curve, representing the data set’s total frequency. This method is the most widely used method of presenting grouped frequency distribution. An alternative to a histogram, frequency polygon can be made with or without constructing a histogram.

• Frequency Curve – The frequency curve is created by drawing smooth, freehand curves instead of straight lines. The frequency curve passes through the points of the frequency polygon. While it is not necessary to pass through all the points of the frequency polygon, the curve is obtained by passing through the points as closely as possible. The shape of the frequency distribution curve is U or inverse U shaped.

• Ogive – Ogive is also known as cumulative frequency curve. Since there are two categories of cumulative frequencies – “less than” and “more than,” ogives for any grouped frequency data are also drawn in two types. While for the ‘less than’ ogives, the cumulative frequencies are plotted against upper limits of the class interval, for ‘more than’ ogives, they are plotted against the lower limits of class intervals. The shape of ‘less than’ ogive rises upward, whereas the shape of ‘more than’ ogive falls downwards. Interestingly, the intersection point of two ogives gives the median.

• Cumulative Frequency – Frequency means the number of times an event has occurred or variables of the different class intervals. Cumulative frequency is the total of frequencies up to a point. It helps identify the sum total of frequencies falling under or beyond a particular class or group of data.)

• Arithmetic Line Graph – Also known as time-series graphs, the arithmetic line graphs are drawn to show trends and periodicity for long time-series data. They are often used for data sets corresponding to weeks, months, and years. They show the arithmetic values of a variable on a graph. While the time is plotted on the X-axis, the variables are placed along the Y-axis of the graph. After plotting the points, a line graph is drawn, joining the plotted points to construct an arithmetic line graph.

Conclusion 

To conclude, frequency diagrams are diagrammatic representations of frequency distributions. They help us derive the trends and patterns of frequency variables at different class interval levels. Very complex data sets can be exhibited by using frequency diagrams to illustrate them clearly. The various types of frequency diagrams are histogram, frequency polygon, frequency curve, ogive, and arithmetic line graph. Frequency diagrams help represent the data sets in a meaningful, comprehensive, and purposeful way.