Frequency Polygon: Meaning, Steps to Draw and Examples

What is Frequency Polygon?

A wave polygon is different measurement to show a wave distribution connected a graph. In summation to being an alternate for The histogram, the frequency polygon is besides an outcome of The histogram. While comparing 2 aliases much wave distributions, a wave polygon is much suitable than utilizing a histogram. Polygons Can beryllium constructed for some discrete and continuous series.

(I) Frequency Polygon in Discrete Series

The steps required to conception a wave polygon in The lawsuit of discrete bid are: 

Step 1: Write The values of The fixed adaptable (say, X) connected The X-axis and The corresponding frequencies connected The Y-axis.

Step 2: Draw a consecutive statement connecting The points of The various frequencies.

Step 3: Extend The fig to the base (base-line) astatine some ends by connecting The utmost points (first and past point) to The 2 hypothetical values of The adaptable (prior to The first worth of The adaptable and aft The past worth of The variable), some of which are assumed to person zero frequency.

Example: 

The pursuing information shows The number of shops connected 70 streets in a city. Construct a wave polygon for The same.

Solution:

The discrete wave distribution applies in this case. The number of rooms will beryllium plotted connected The X-axis, while The number of houses will beryllium plotted connected The Y-axis. A wave polygon is created by joining The obtained points pinch a consecutive line.

(II) Frequency Polygon in Continuous Series

There are 2 ways of creating a wave polygon for a continuous wave distribution:

(i) With The thief of a Histogram
(ii) Without The thief of a Histogram

(A) Frequency Polygon pinch The thief of a Histogram:

The steps required to conception a wave polygon in The lawsuit of continuous bid pinch The thief of a histogram are: 

Step 1: Create a histogram for The given frequency distribution.

Step 2: Connect The mid-points of The tops (upper horizontal sides) of The adjacent rectangles of The histogram pinch consecutive lines.

Step 3: Close The fig by extending The 2 ends to The base-line. In bid to do so, 2 hypothetical classes from either extremity would person to beryllium included, each pinch a zero frequency.

Example: 

The pursuing is The property distribution of members in a associated family. Create a histogram from this information and person it to a wave polygon.

Solution:

The continuous wave distribution applies in this case, arsenic location is simply a wave distribution pinch adjacent people intervals. Firstly, The histogram is prepared, and past The wave polygon. The property of The members will beryllium plotted connected The X-axis, while The number of family members will beryllium plotted connected The Y-axis.

(B) Frequency Polygon without The thief of a Histogram:

The steps required to conception a wave polygon in The lawsuit of continuous bid without The thief of a histogram are: 

Step 1: Take The midpoints of The X-axis for people intervals and The Y-axis for frequency.

Step 2: Plot The different frequencies, joining The points pinch a consecutive line.  

Step 3: Assuming that The frequencies are zero, The obtained figure is extended to The guidelines astatine some ends by connecting The utmost points (first and last points) to The midpoints of The 2 hypothetical classes (before the first people and aft the last class). 

The resulting figure, in this case, would beryllium The aforesaid arsenic in The supra illustration (with a histogram). The only quality is that location is nary request of creating The histogram. 

What is Frequency Curve?

A wave curve is simply a consequence of joining The vertices of a wave polygon pinch a soft curve. It is also referred to arsenic a Smoothed Frequency Curve. The wave curve whitethorn not ever spell done each of The points of The wave polygon, but it passes done them as intimately arsenic possible.

• A wave curve should beryllium cautiously constructed to debar crisp edges.
• The curve is drawn freehand in a measurement that makes The area covered astir adjacent to that of The polygon.
• This curve should statesman and extremity astatine The baseline. It is usually extended to The mediate constituent of The people interval extracurricular of The histogram.
• The full number of frequencies in The full distribution should beryllium represented by The area nether The curve.

Steps of Frequency Curve 

Step 1: Using The fixed data, create a histogram. 

Step 2: Determine The midpoints of The precocious horizontal broadside of each rectangle. 

Step 3: To create a wave curve, subordinate The mid-points of The adjacent rectangles of The histogram utilizing a soft free hand. 

Step 4. With a free hand, widen The ends of The wave curve to The baseline.

Example: 

Draw a wave curve from The pursuing distribution.

Solution:

The continuous wave distribution applies in this case, arsenic location is simply a wave distribution pinch adjacent people intervals. Firstly, The histogram is prepared, and past The wave curve. The people interval will beryllium plotted connected The X-axis, while The wave distribution will beryllium plotted connected The Y-axis.

Last Updated : 11 May, 2023

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