Assignment 02
On
MERITS AND DEMERITS OF STATISTICS TERM
Course Title: Business Statistics
Course Code: MBM 507
First Year, Term – II, 2014
Submitted To:
Tofayel Ahmed
Lecturer
Submitted By:
A. K. M. Ezazul Haque
Roll: 171318
17th Batch
Date of Submission: February 10, 2014
1.0 MERITS AND DEMERITS OF ARITHEMETIC MEAN
1.1 Merits of Arithmetic Mean

Arithmetic mean rigidly defined by algebraic formula

It is easy to calculate and simple to understand

it based on all observations and it can be regarded as representative of the given data

It is capable of being treated mathematically and hence it is widely used in statistical
analysis.

Arithmetic mean can be computed even if the detailed distribution is not known but some
of the observation and number of the observation are known.

It is least affected by the fluctuation of sampling
1.2 Demerits or Limitations of Arithmetic Mean

It can neither be determined by inspection or by graphical location

Arithmetic mean cannot be computed for qualitative data like data on intelligence
honesty and smoking habit etc

It is too much affected by extreme observations and hence it is not adequately represent
data consisting of some extreme point

Arithmetic mean cannot be computed when class intervals have open ends
2.0 MERITS AND DEMERITS OF GEOMETRIC MEAN (GM)
2.1 Merits of Geometric Mean

It is based on all the items of the data.

It is rigidly defined. It means different investigators will find the same result from the
given set of data.

It is a relative measure and given less importance to large items and more to small ones
unlike the arithmetic mean.

Geometric mean is useful in ratios and percentages and in determining rates of increase
or decrease.

It is capable of algebraic treatment. It mean we can find out the combined geometric
mean of two or more series.
2.2 Demerits or Limitations of Geometric Mean

It is not easily understood and therefore is not widely used.

It is difficult to compute as it involves the knowledge of ratios, roots, logs and antilog.

It becomes indeterminate in case any value in the given series happen to be zero or
negative.

With open-end class intervals of the data, geometric mean cannot be calculated.

Geometric mean may not correspond to any value of the given data.
3.0 MERITS AND DEMERITS OF HARMONIC MEAN
3.1 Merits Of Harmonic Mean

It is rigidly defined average and its value is always definite.

Its value is based on all observation in a given series.

It is capable of further algebraic treatment.

It is not affected by sampling fluctuations.

In problems relating to time and rates, it gives better results as compared to other
averages. Harmonic mean gives the best result when distance covered are the same, but
speed of coverage varies.
3.2 Demerits or Limitations of Harmonic Mean

It is not easily understood and hence its application is ignored.

It is not easy to calculate as it involves reciprocal values (The use of calculators can help
to remove this difficulty).

It gives undue weights to small items and ignores bigger items. This restricts its use in the
analysis of economic data.

In case of zero or negative values, it cannot be computed.
4.0 MERITS AND DEMERITS OF MEDIAN
4.1 Merits Of Median

Median is rigidly defined as in the case of Mean.

Even if the value of extreme item is much different from other values, it is not much
affected by these values e.g. median in case of 4, 7, 12, 18, 19 is 12 and if we add two
values equal to 450 10000, new median is 18.

It can also be used for the Quantities; those can't give A.M; as is in case of intelligence
etc. It is possible to arrange in any order and to locate the middle value. For such cases it
is the best measure.

It can be located graphically.

For open end intervals, it is also suitable one. As taking any value of the intervals, value
of Median remains the same.

It can be easily calculated and is also easy to understand.

Median is also used for other statistical devices such as Mean Deviation and skewness.

It can be located by inspection in some cases.

Extreme items may not be available to get Median.
4.2 Demerits or Limitations Of Median

Even if the value of extreme items is too large, it does not effect too much, but due to this
reason, sometimes median does not remain the representative of the series.

It is affected much more by fluctuations of sampling than A.M.

Median cannot be used for further algebraic treatment. Unlike mean we can neither find
total of terms as in case of A.M. nor median of some groups when combined.

In a continuous series it has to be interpolated. We can find its true-value only if the
frequencies are uniformly spread over the whole class interval in which median lies.

If the number of series is even, we can only make its estimate; as the A.M. of two middle
terms is taken as Median.
5.0 MERITS AND DEMERITS OF MODE
5.1 Merits of mode

Mode is very simple measure of central tendency. Sometimes, just at the series is enough
to locate the model value. Because of its simplicity, it s a very popular measure of the
central tendency.

Compared top mean, mode is less affected by marginal values in the series. Mode is
determined only by the value with highest frequencies.

Mode can be located graphically, with the help of histogram.

Mode is that value which occurs most frequently in the series. Accordingly, mode is the
best representative value of the series.

The calculation of mode does not require knowledge of all the items and frequencies of a
distribution. In simple series, it is enough if one knows the items with highest frequencies
in the distribution.
5.2 Demerits of mode

Mode is an uncertain and vague measure of the central tendency.

Unlike mean, mode is not capable of further algebraic treatment.

With frequencies of all items are identical, it is difficult to identify the modal value.

Calculation of mode involves cumbersome procedure of grouping the data. If the extent
of grouping changes there will be a change in the model value.

It ignores extreme marginal frequencies. To that extent model value is not a
representative value of all the items in a series.
6.0 MERITS AND DEMERITS OF RANGE
6.1 Merits or Uses of Range

It is easiest to calculate and simplest to understand even for a beginner.

It is one of those measures which are rigidity defined.

It gives us the total picture of the problem even with a single glance.

It is used to check the quality of a product for quality control. Range plays an important
role in preparing R- charts, thus quality is maintained.

The idea about the price of Gold and Shares is also made taking care of the range in
which prices have moved for the past some periods.

Meteorological Department also makes forecasts about the weather by keeping range of
temp.
6.2 Demerits or Limitations or Drawbacks of Range

Range is not based on all the terms. Only extreme items reflect its size. Hence range
cannot be completely representative of the data as all other middle values are ignored.

Due to above reason range is not a reliable measure of dispersion.

Range does not change even the least even if all other, in between, terms and variables
are changed.

Range is too much affected by fluctuation of sampling. Range changes from sample to
sample. As the size of sample increases range increases and vice versa.

It does not tell us anything about the variability of other data.

For open-end intervals, range is indeterminate because lower and appear limits of first
and last interval are not given.
7.0 MERITS AND DEMERITS OF QUARTILE DEVIATION
7.1 Merits of Quartile Deviation

It can be easily calculated and simply understood.

It does not involve much mathematical difficulties.

As it takes middle 50% terms hence it is a measure better than Range and percentile
Range.

It is not affected by extreme terms as 25% of upper and 25% of lower terms are left out.

Quartile Deviation also provides a short cut method to calculate Standard Deviation using
the formula 6 Q.D. = 5 M.D. = 4 S.D.

In case we are to deal with the centre half of a series this is the best measure to use.
7.2 Demerits or Limitations of Quartile Deviation

As Q1 and Q3 are both positional measures hence are not capable of further algebraic
treatment.

Calculation is much more, but the result obtained is not of much importance.

It is too much affected by fluctuations of samples.

50% terms play no role; first and last 25% items ignored may not give reliable result.

If the values are irregular, then result is affected badly.

We can't call it a measure of dispersion as it does not show the scatter-ness around any
average.

The value of quartile may be same for two or more series or Q.D. is not affected by the
distribution of terms between Q1 and Q3 or outside these positions.
8.0 MERITS AND DEMERITS OF STANDARD DEVIATION
8.1 Merits of Standard Deviation

Standard deviation is rigidly defined and its value is always definite.

It is based on all the observation of the data.

It is amenable to algebraic treatment and possesses many mathematical properties. It is on
account of these properties that standard deviation is used in many advanced studies.

It is less affected by the fluctuations of sampling than most other measures of dispersion.

The squaring of deviations makes them positive and the difficulty about algebraic signs
which was experienced in case of mean deviation is not found here.
8.2 Demerits of Standard Deviation

Standard deviation is not easy to calculate, nor is it easily understood. In any case it is
more cumbersome in its calculation than either quartile deviation or mean deviation.

It gives more weight to extreme items and less to those which are near the mean, because
the squares of the deviations, which are big in size, would be proportionately greater than
the squares of those deviations which are comparatively small. Thus, deviation 2 and 8
are in the ratio of 1:4 but their square i.e, 4 and 64 would be in the ratio of 1:16.
9.0 MERITS AND DEMERITS OF MEAN DEVIATION
9.1 Merits of Mean Deviation

As in case of X, every term is taken in account hence, it is certainly a better measure than
other measures of dispersion i.e. Range, Percentile Range or Quartile Range.

Mean deviation is extensively used in other fields such as Economics, Business,
Commerce or any other field of such type.

It has least sampling fluctuations as compared to Range, Percentile Range and Quartile
Deviation.

When comparison is needed this is perhaps the best measure between two or more series.

This calculation has its base upon measurement than an estimate.

Mean Deviation is rigidly defined; one of the main focus point of any measure used for
statistical Analysis.

It we calculate it from median it is less affected by extreme terms.

As it is based on the deviations about an average, it gives us better measure for
comparison.
9.2 Demerits or Limitations or Drawbacks of Mean Deviation

If average is in fractions, it is difficult to compile M.D.

Main property is absent, It is not capable of further Algebraic Treatment.

Not so easy to calculate to calculate X, M or Z first and then to go for other measures.

If it is calculated from Z it is not much reliable as Mode (Z) is not the true representative
of the series.

M.D. and its co-efficient taken from X, M and Z often differ.

As +- signs are ignored which is not possible mathematically. Algebraically we have to
proceed for Standard Deviation; or another measure of dispersion.

As for mean, open and series cannot be taken for the true result.

If Range increases in case the sample increases, Average deviation also increases but not
in the same ratio.

For Sociological studies, it is almost not used.