They are usually expressed in percentage form.
Principles for Constructing Frequency Distributions Inspite of the great importance of classification in statistical analysis, no hard and fast rules are laid down for it. A statistician uses his discretion for classifying a frequency distribution and sound experience, wisdom, skill and aptness for an appropriate classification of the data.
However, the following guidelines must be considered to construct a frequency distribution: The classes should be clearly defined and should not lead to any ambiguity.
They should be exhaustive and mutually exclusive so that any value of variable corresponds to only class. The choice about the number of classes in which a given frequency distribution should be divided depends upon the following things; i The total frequency which means the total number of observations in the distribution.
The number of classes should not be too small or too large. If the classes are few, the classification becomes very broad and rough which might obscure some important features and characteristics of the data.
The accuracy of the results decreases as the number of classes becomes smaller. On the other hand, too many classes will result in a few frequencies in each class. This will give an irregular pattern of frequencies in different classes thus makes the frequency distribution irregular.
Moreover a large number of classes will render the distribution too unwieldy to handle. The computational work for further processing of the data will become quite tedious and time consuming without any proportionate gain in the accuracy of the results.
Hence a balance should be maintained between the loss of information in the first case and irregularity of frequency distribution in the second case, to arrive at a suitable number of classes. Normally, the number of classes should not be less than 5 and more than Sturges has given a formula: Further, the number or class intervals should be such that they give uniform and unimodal distribution which means that the frequencies in the given classes increase and decrease steadily and there are no sudden jumps.
The number of classes should be an integer preferably 5 or multiples of 5, 10, 15, 20, 25 etc. Size of Class Intervals: Because the size of the class interval is inversely proportional to the number of classes in a given distribution, the choice about the size of the class interval will depend upon the sound subjective judgment of the statistician.
If 6 is the estimate of population standard deviation then the length of class interval is given by: The size of class intervals should be taken as 5 or multiples of 5, 10, 15 or 20 for easy computations of various statistical measures of the frequency distribution, class intervals should be so fixed that each class has a convenient mid-point around which all the observations in that class cluster.
It means that the entire frequency of the class is concentrated at the mid value of the class. It is always desirable to take the class intervals of equal or uniform magnitude throughout the frequency distribution.
If in a grouped frequency distribution there are gaps between the upper limit of any class and lower limit of the succeeding class as in case of inclusive type of classificationthere is a need to convert the data into a continuous distribution by applying a correction factor for continuity for determining new classes of exclusive type.
Let us consider the following example to understand: Marks Class Boundaries 20—24 20—0. Mid-value or Class Mark:Thus index numbers are used to measures all types of quantitative changes in the agricultural, industrial, and commercial fields, as also in such economic magnitudes .
1) Index numbers are used as economic barometers: Index number is a special type of averages which helps to measure the economic fluctuations on price level, 5/5(6). For Economists, index numbers are of use at every stage of planning, policy making, decision making etc.
and so, index numbers may very be called ‘Economic Barometers’. Just as Barometers measure atmospheric pressure, index numbers measure changes occurring in economic field.
It is quite common for a stock index or exchange to be used as a barometer for national economic health. Barometers can also be used to measure behavior at the consumer level.
For example, slowing. In reality, Index Numbers are described as barometers of economic activity because if one wants to have an idea as to what is happening in an economy, he should check the important indicates like the index numbers of industrial production, agricultural production, business activity etc.
Why Index Numbers Are Also Called Economic Barometers Importance of Index Number in Business Introduction: An index number is a statistical device for comparing the general level of magnitude of a group of related variables in two or more situation.