{"id":2767,"date":"2023-03-28T09:00:25","date_gmt":"2023-03-28T03:30:25","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2767"},"modified":"2023-03-28T09:51:45","modified_gmt":"2023-03-28T04:21:45","slug":"cumulative-frequency-curve-ogive-statistics","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/cumulative-frequency-curve-ogive-statistics\/","title":{"rendered":"What is Cumulative Frequency Curve or the Ogive in Statistics"},"content":{"rendered":"

What is Cumulative Frequency Curve or the Ogive\u00a0in Statistics<\/strong><\/h2>\n

First we prepare the cumulative frequency table, then the cumulative frequencies are plotted against the upper or lower limits of the corresponding class intervals. By joining the points the curve so obtained is called a cumulative frequency curve or ogive<\/strong>.
\nThere are two types of ogives :<\/p>\n

    \n
  1. Less than ogive : <\/strong>Plot the points with the upper limits of the class as abscissae and the corresponding less than cumulative frequencies as ordinates. The points are joined by free hand smooth curve to give less than cumulative frequency curve or the less than Ogive. It is a rising curve.<\/li>\n
  2. Greater than ogive :<\/strong> Plot the points with the lower limits of the classes as abscissa and the corresponding Greater than cumulative frequencies as ordinates. Join the points by a free hand smooth curve to get the “More than Ogive”. It is a falling curve.<\/li>\n<\/ol>\n

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    When the points obtained are joined by straight lines, the picture obtained is called cumulative frequency polygon.
    \nLess than ogive method:<\/strong>
    \nTo construct a cumulative frequency polygon and an ogive by less than method, we use the following algorithm.
    \nAlgorithm<\/strong>
    \nStep 1 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Start with the upper limits of class intervals and add class frequencies to obtain the cumulative frequency distribution.
    \nStep 2 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Mark upper class limits along X-axis on a suitable scale.
    \nStep 3 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Mark cumulative frequencies along Y-axis on a suitable scale.
    \nStep 4 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Plot the points (xi, fi) where xi\u00a0is the upper limit of a class and fi\u00a0is corresponding cumulative frequency.
    \nStep 5 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Join the points obtained in step 4 by a free hand smooth curve to get the ogive and to get the cumulative frequency polygon join the points obtained in step 4 by line segments.<\/p>\n

    More\u00a0than ogive method:<\/strong>
    \nTo construct a cumulative frequency polygon and an ogive by more than method, we use the following algorithm.
    \nAlgorithm<\/strong>
    \nStep 1 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Start with the lower limits of the class intervals and from the total frequencysubtract the frequency of each class to obtain the cumulative frequency distribution.
    \nStep 2 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Mark the lower class limits along X-axis on a sutiable scale.
    \nStep 3 : \u00a0 \u00a0\u00a0<\/strong>Mark the cumulative frequencies along Y-axis on a suitable scale.
    \nStep 4 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Plot the points (xi, fi) where xi\u00a0is the lower limit of a class and fi\u00a0is corresponding cumulative frequency.
    \nStep 5 :<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0Join the points obtained in step 4 by a free hand smooth curve to get the ogive and to get the cumulative frequency polygon join these points by line segments<\/p>\n

    Read \u00a0More:<\/strong><\/p>\n