Frequency Diagrams

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FREQUENCY DIAGRAMS :

FREQUENCY DIAGRAMS HISTOGRAM, POLYGON AND OGIVE

FREQUENCY DIAGRAMS :

FREQUENCY DIAGRAMS Frequency diagrams relate to diagrammatic presentation of “frequency distribution”. In such series, values of a variable repeat themselves number of times. That is, different values of a variable happen to occur different number of times. There are three important forms of frequency diagrams :- Histogram Polygon Ogive

1. HISTOGRAM:

1. HISTOGRAM A histogram is a graphical presentation of a frequency distribution of a continuous series. It is a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval . Origin :

If frequencies are expressed in terms of percentage in the distribution, then the same are shown as percentage on the graph instead of the number of items. Histograms of frequency distribution are of two types : :

If frequencies are expressed in terms of percentage in the distribution, then the same are shown as percentage on the graph instead of the number of items. Histograms of frequency distribution are of two types : Histograms of equal class intervals Histograms of unequal class intervals

Histogram of equal class intervals:

Histogram of equal class intervals

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Histogram of equal class intervals are those which are based on the data with equal class intervals. A series with equal class intervals would make a histogram including rectangles of equal width . Length of the rectangles would be different in proportion to the frequencies of the class intervals.

Histogram of unequal class intervals:

Histogram of unequal class intervals

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A histogram of unequal class interval is the one which is based on the data with unequal class intervals. When the data of class intervals are unequal, width of the rectangles would be different. The width of the rectangles would increase or decrease depending upon the increase and decrease in the size of the class intervals. Before, presenting the data in the form of graphs , frequencies of unequal class-intervals are adjusted. ADJUSTMENT FACTOR FOR ANY CLASS= Class interval of the concerned class lowest class interval

2.POLYGON:

2.POLYGON Polygon is another form of diagrammatic presentation of data. It is formed by joining mid-points of the tops of all rectangles in a histogram. However, a polygon can be drawn without constructing a histogram. F or this, mid-values of the classes of a frequency distribution are marked on X-axis of the graph; the corresponding frequencies are marked on the Y-axis. Using a foot rule, all points indicating frequencies of the different classes are joined to make a graph, called frequency polygon.

Difference between histogram and frequency polygon?:

Difference between histogram and frequency polygon? A histogram becomes a frequency polygon if we draw a line joining mid-points of the tops of all rectangles in a histogram.it is important that the mid-points are joined using a foot-rule to make a straight line.

Frequency polygon with histogram:

Frequency polygon with histogram

Frequency polygon without histogram:

Frequency polygon without histogram

3.FREQUENCY CURVE:

3.FREQUENCY CURVE It is just a variant of polygon. A frequency curve is a curve which is plotted by joining the mid-points of all tops of a histogram by freehand smoothed curves and not by straight lines. Area of a frequency curve is equal to the area of a histogram or frequency polygon of a given data set. While drawing a frequency curve , we should eliminate angularity of the polygon. Accordingly, points of a frequency polygon are joined through a freehand smoothed curve rather than a straight lines.

Basic difference between a frequency polygon and a frequency curve:

Basic difference between a frequency polygon and a frequency curve Both frequency polygon and frequency curve are drawn by joining the mid-points of all tops of a histogram. B ut in case of frequency polygon the points are joined using a foot rule {to make a straight line}, whereas in case of frequency curve the points are joined using a freehand.

4. OGIVE OR CUMULATIVE FREQUENCY CURVE:

4 . OGIVE OR CUMULATIVE FREQUENCY CURVE Ogive or Cumulative frequency curve is the curve which is constructed by plotting cumulative frequency data on the graph paper, in the form of a smooth curve.

Cumulative frequency curve or ogive may be constructed in two ways::

Cumulative frequency curve or ogive may be constructed in two ways:

The basic difference between “less than” and “more than” ogives:

The basic difference between “less than” and “more than” ogives In less than ogives , frequencies are added starting starting from the upperlimit of the 1 st class interval of the frequency distribution. On the other hand , in case of ‘more than’ ogives , frequencies are added starting from the lower limit of the 1 st class interval of the frequency distribution. Accordingly, while in case of ‘less than’ ogive the cumulative total tends to increase, in case of ‘more than’ ogive , the cumulative total tends to decrease.0

Different shapes of frequency curves:

Different shapes of frequency curves

1. NORMAL CURVE OR SYMMETRICAL CURVE:

1. NORMAL CURVE OR SYMMETRICAL CURVE In such curves, frequencies tend to increase gradually, followed by the tendency to stabilize and finally the tendency to decline.

2. POSITIVE SKEWED CURVE:

2. POSITIVE SKEWED CURVE In such curves, curves are skewed to right side more than the left one. Curves have more spread on the right side. That is, these are tailed to right side.

3. NEGATIVE SKEWED CURVE:

3. NEGATIVE SKEWED CURVE In such curves, the curve is skewed to the left. That is, such curves are tailed to the left.

4. U- SHAPED CURVE:

4. U- SHAPED CURVE U-shaped curves are formed if there are two high points in a series both having equal or nearly equal frequency, at the lowest and highest values.

5.BI-MODAL CURVE:

5.BI-MODAL CURVE This curve is drawn when, in a series, there are two classes with highest frequencies.

6. J-SHAPED CURVE:

6. J-SHAPED CURVE This curve is drawn when, in a distribution, frequencies tend to increase with each class interval. In other words the curve moves from the low frequencies to the high frequencies.

7. REVERSE J-SHAPED CURVE:

7. REVERSE J-SHAPED CURVE This type of curve is drawn when there are highest frequencies corresponding to lowest values in distribution.

8. MIXED CURVE OR MULTI-MODAL CURVE:

8. MIXED CURVE OR MULTI-MODAL CURVE These curves are formed when there is no specific pattern of the frequencies corresponding to different values ( or classes) in the given distribution.

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