Lecture 5/ Harmonic and Geometric Means/2018- 2019 /

Merits of Geometric Mean
1. It is based upon all values of the given data.
2. It is capable of further mathematical treatment.
3. It is not much affected by sampling fluctuations.
Demerits of Geometric Mean
1. It is not easy to understand & not easy to calculate
2. It is not well defined.
3. If anyone data value is zero then GM is zero.
4. It cannot be calculated if any observations are missing.
5. It cannot be calculated for the data with open end classes.
6. It is affected by extreme values.
7. It cannot be located graphically.
8. It may be number which is not present in the data.
9. It cannot be calculated for the data representing qualitative characteristic
Merits of Harmonic Mean
1. It is rigidly defined.
2. It is easy to understand & easy to calculate.
3. It is based upon all values of the given data.
4. It is capable of further mathematical treatment.
5. It is not much affected by sampling fluctuations.
Demerits of Harmonic Mean
1. It is not easy to understand & not easy to calculate.
2. It cannot be calculated if any observations are missing.
3. It cannot be calculated for the data with open end classes.
4. It is usually not a good representative of the data.
5. It is affected by extreme values.
6. It cannot be located graphically.
7. It may be number which is not present in the data.
8. It can be calculated for the data representing qualitative characteristic.

Selection of an average:
No single average can be regarded as the best or most suitable under all circumstances. Each
average has its merits and demerits and its own particular field of importance and utility. A
proper selection of an average depends on the 1) nature of the data and 2) purpose of enquiry or
requirement of the data.
A.M. satisfies almost all the requisites of a good average and hence can be regarded as the
best average but it cannot be used
1) in case of highly skewed data.
2) in case of uneven or irregular spread of the data.
3) in open end distributions.
4) When average growth or average speed is required.
5) When there are extreme values in the data.

Except in these cases AM is widely used in practice.
Median: is the best average in open end distributions or in distributions which give highly skew or
j or reverse j type frequency curves. In such cases A.M. gives unnecessarily high or low
value whereas median gives a more representative value. But in case of fairly symmetric
distribution there is nothing to choose between mean, median and mode, as they are very
close to each other.
Mode : is especially useful to describe qualitative data. According to Freunel and William