The statistical data can be represented graphically. Graphical representation of data helps in faster and easier interpretation of data.

#### Frequency polygon

Drawing a Frequency polygon using a histogram

- Draw the histogram for the given frequency distribution
- Take the mid-points of the upper horizontal side of each rectangle
- Take the mid-points of two imaginary class intervals, one on either side of the histogram
- Join these mid-points by line segments one after the other

#### Frequency polygon by not using a histogram

- Make an exclusive frequency distribution table
- Find the class marks of all the class intervals
- Mark the point </mo><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><mspace width="thinmathspace" /><msub><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false"></mo></math>">(x1,y1)(x1,y1) on the graph, where x1 denotes the class mark and y1 denotes the corresponding frequency
- Join all the points plotted above with straight line segments
- Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution

#### Ogives

Steps for construction:

- Construct a cumulative frequency table.
- Mark the actual class limits along x-axis and the cumulative frequencies of the respective classes along y-axis by using suitable scale.
- Plot the points such that the x coordinate is the upper limit of the class interval and the y-coordinate is the corresponding cumulative frequency
- Join the plotted points by a free hand curve.

Less than Ogive

- Less than type “ogive” curve is obtained by plotting the cumulative frequency on the Y-axis and the upper limits of the class intervals on the X-axis

More than Ogive

- More than type “ogive” is obtained by plotting the cumulative frequency on the Y-axis and the lower limits of the class intervals on the X-axis

The statistical data can be represented graphically. Graphical representation of data helps in faster and easier interpretation of data.

#### Frequency polygon

Drawing a Frequency polygon using a histogram

- Draw the histogram for the given frequency distribution
- Take the mid-points of the upper horizontal side of each rectangle
- Take the mid-points of two imaginary class intervals, one on either side of the histogram
- Join these mid-points by line segments one after the other

#### Frequency polygon by not using a histogram

- Make an exclusive frequency distribution table
- Find the class marks of all the class intervals
- Mark the point </mo><msub><mi>x</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>,</mo><mspace width="thinmathspace" /><msub><mi>y</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo stretchy="false"></mo></math>">(x1,y1)(x1,y1) on the graph, where x1 denotes the class mark and y1 denotes the corresponding frequency
- Join all the points plotted above with straight line segments
- Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution

#### Ogives

Steps for construction:

- Construct a cumulative frequency table.
- Mark the actual class limits along x-axis and the cumulative frequencies of the respective classes along y-axis by using suitable scale.
- Plot the points such that the x coordinate is the upper limit of the class interval and the y-coordinate is the corresponding cumulative frequency
- Join the plotted points by a free hand curve.

Less than Ogive

- Less than type “ogive” curve is obtained by plotting the cumulative frequency on the Y-axis and the upper limits of the class intervals on the X-axis

More than Ogive

- More than type “ogive” is obtained by plotting the cumulative frequency on the Y-axis and the lower limits of the class intervals on the X-axis

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