Confidence Interval Formula Confidence Interval Formula In mathematics we know the graphical representation of frequency distribution that is done by using the bar graphs, histograms and frequency polygons. The Ogiveis also known as the names of cumulative frequency curves that are the continuous. Generally the techniques of drawing the cumulative frequency polygons and cumulative frequency curves or ogive are more or less the same. The only difference is that in case of simple frequency curves and polygons the frequencies are plotted against class marks of the class intervals where as in case of a cumulative frequency polygon or curves the cumulative frequencies are plotted against the lower or upper limits of the class intervals depending upon the manner in which the series has been cumulated. There are two methods of constructing a frequency polygon and an ogive. Let us now discuss the two methods. I.
Less than method
II.
More than method
1. Less than method: - To construct an ogive by less than method, we use the following algorithm. Know More About Standard Deviation Formula Math.Tutorvista.com
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Algorithm Step 1 : - Start with the upper limits of class intervals and add class frequencies to obtain the cumulative frequency distribution. Step 2 : - Mark upper class limits along X-axis on a suitable scale. Step 3 : - Mark cumulative frequencies along Y-axis on a suitable scale. Step 4 : - Plot the points (xi, fi ) where xi is the upper limit of a class and fi is corresponding cumulative frequency. Step 5 : - Join the points obtained in step 4 by a free hand smooth curve to get the ogive. 2. More than method: - To construct an ogive by more than method, we use the following algorithm. Algorithm Step 1 : - Start with the lower limits of class intervals and from the total frequency subtract the frequency of each class to obtain the cumulative frequency distribution. Step 2 : - Mark the lower class limits along X-axis on a suitable scale. Step 3 : - Mark the cumulative frequencies along Y-axis on a suitable scale. Step 4 : - Plot the points (xi, fi ) where xi is the lower limit of a class and fi is corresponding cumulative frequency. Step 5 : - Join the points obtained in step 4 by a free hand smooth curve to get the ogive.
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Some application of ogive : - Ogive s can be used to find the median of frequency distribution. In order to determine the same, we may use following algorithms. Algorithm 1 Step 1 : - Draw anyone of the two types of frequency curves on the graph paper. Step 2 : - Compute N / 2 (N = ∑fi) and mark the corresponding point on y-axis. Step 3 : - Draw a line parallel to x-axis, from the point marked in step 2., cutting the cumulative frequency curve at a point P (say). Step 4 : - Draw perpendicular PM from P on the X-axis. The x coordinate of point M gives the median. Algorithm 2 Step 1 : - Draw less than type or greater than type cumulative frequency curves on the graph paper. Step 2 : - Mark the point of intersection of the two curves drawn in step 1. let this point be P. Step 3 : - Draw perpendicular PM from P on the X-axis. The x coordinate of point M gives the median
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