FREQUENCY DIAGRAMS



SECOND TERM

FREQUENCY DIAGRAMS

Frequency diagrams are used to represent data in the form of grouped frequency distribution.

Kinds of frequency graphs

• Histogram

• Frequency polygon

• Frequency curve

• Cumulative frequency curves

• Arithmetic line graphs

Histogram – is a two dimensional diagram. It is a set of adjacent rectangles with class interval as the base and frequencies as the height of the rectangles.

Histograms of frequency distribution are of two types:

• histogram with equal class interval

• histogram with unequal class width

Histogram with equal class intervals are drawn with frequencies as the height of the triangles and class width as width of the triangle.

Construction of histogram when class intervals are unequal-

When class intervals are unequal, the frequencies are to be adjusted before constructing the histogram. Adjustments are done as follows

1. Find the adjustment factor by dividing the class width of each class by the class interval of the lowest class

2. Divide the frequency of each class by the corresponding adjustment factor to get the frequency density.

3. Construct the histogram with frequency density as the height of the rectangle and class intervals as the base of the triangle

• (Note; if the frequency distribution is inclusive, convert them into exclusive

• If mid values are given, find out the lower and upper limits of the various classes before constructing the histogram.)

Frequency polygon

Frequency polygon can be drawn in two different ways.

Method 1- draw the histogram of the given data and then join the mid point of the upper horizontal sides of each rectangle with the help of a ruler.

Method 2 –Plot the frequencies against the mid points of various classes and join all the points with a ruler.

Frequency curve

Frequency curves are constructed by joining the mid points of a histogram by free hand curves.

Ogives or cumulative frequency curves

Cumulative frequency curves are of two types ;

A) Less than cumulative frequency curve

B) Greater than cumulative frequency curve

For the construction of less than ogive, the cumulative frequencies are plotted along y axis against upper limits of the frequency distribution.

For greater than ogive the cumulative frequencies are plotted along y axis against lower limits of the frequency distribution

Arithmetic line graph (time series graph)

Under this time is plotted along the X axis and the values of the variables along y - axis

Plotted points are joined to get the line graph.

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Difference between a bar graph and histogram –

• Bar diagrams e one dimensional where as histograms are two dimensional

• Bar diagrams can be drawn for both discrete and continuous variables, but histogram is drawn only for a continuous variable

• In a bar diagram space is left between consecutive bars, in histogram rectangles are drawn adjacent to one another.

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Relationship between histogram and frequency polygon

1. the area under the frequency curve , over any class interval is proportional to the frequency of that class

2. area under the histogram is equal to area under frequency polygon

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Rules for constructing graph

• Heading – every graph should have a suitable heading which is self explanatory

• Choice of scale –an appropriate scale should be fixed for both X and Y axis

• False base line – should be used if the size of the smallest variable in the series is large.

Numerical questions

1. Represent the following data relating to gross annual profits of a company graphically

|year |1998 |1999 |2001 |2002 |2003 |2004 |

|Profit in |60 |72 |75 |65 |80 |95 |

|thousands | | | | | | |

2. Draw a histogram and frequency polygon for the following

|class |10-15 |15-20 |20-25 |25-30 |30-35 |35-40 |40-45 |

|frequency |4 |6 |7 |12 |1 |16 |5 |

3. Construct a histogram and frequency curve

|midpoint |115 |125 |135 |145 |155 |165 |

|frequency |5 |7 |12 |20 |16 |10 |

5. Find the number of workers earning less than rupees 50 per week, with the help of an appropriate frequency curve

|Weekly wages |0-20 |20-40 |40-60 |60-80 |80-100 |

|Number of workers |14 |21 |30 |10 |12 |

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