Page 76 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes • A discrete series is obtained from a large number of individual observations. Suppose the marks
obtained by 100 students is given. This data can be converted into a discrete series where the
marks obtained are accompained by the number of students obtaining it.
• The continuous series expresse the data which is very vast. The calculation of arithmetic mean
of this series is similar to that of discrete series after calculating the mid point of each segment
of the continuous series which is called the class interval.
• As distinct from the arithmetic mean which is calculated from the value of every item in the
series, the median is what is called a positional average. The term ‘position’ refers to the place of
a value in a series. The place of the median in a series is such that an equal number of items lie
on either side of it.
• The mode is often said to be the value which occurs most frequently. While this statement is
quite helpful in interpreting the mode, it cannot safely be applied to any distribution, because
of the vagaries of sampling. Even fairly large samples drawn from a statistical population with
a single well-defined mode may exhibit very erratic fluctuations. Hence, mode should be thought
as the value which has the greatest density in its immediate neighbourhood. For this reason mode
is also called the most typical or fashionable value of a distribution.
• Determining the precise value of the mode of a frequency distribution is by no means an
elementary calculation. Essentially, it involves fitting mathematically of some appropriate type
of frequency curve to the grouped data and the determination of the value on the X-axis below
the peak of the curve. However, there are several elementary methods of estimating the mode.
• A distribution having only one mode is called unimodal. If it contains more than one mode, it is
called bimodal or multimodal. In the latter case the value of mode cannot be determined by the
above formula and hence mode is ill-defined. If collected data produce a bimodal distribution,
the data themselves should be questioned. Quite often such a condition is caused when the size
of the sample is small; the difficulty can be remedied by increasing the sample size. Another
common cause is the use of non-homogeneous data. Instances where a distribution is bimodal
and nothing can be done to change it, the mode should not be used as a measure of central
tendency.
• The formula for calculating the value of mode given above is applicable only where there are
equal class intervals. If the class intervals are unequal then we must make them equal before
we start computing the value of mode. The class interval should be made equal and frequencies
adjusted on the assumption that they are equally distributed throughout the class.
5.5 Key-Words

1. Mean : In statistics, mean has three related meanings:
(i) the arithmetic mean of a sample (distinguished from the geometric mean or
harmonic mean).
the expected value of a random variable.
the mean of a probability distribution.

There are other statistical measures of central tendency that should not be confused
with means - including the 'median' and 'mode'. Statistical analyses also commonly use
measures of dispersion, such as the range, interquartile range, or standard deviation.
Note that not every probability distribution has a defined mean; see the Cauchy
distribution for an example.
2. Median: In statistics and probability theory, median is described as the numerical value separating
the higher half of a sample, a population, or a probability distribution, from the lower

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