Arithmetic mean or simply the mean of a variable is defined as the sum of the observations divided by the number of observations. The Merits & demerits of Arithmetic mean are It is rigidly defined. It is easy to understand and easy to calculate. If the number of items is sufficiently large, it is more accurate and more reliable. It is a calculated value and is not based on its position in the series. It is possible to calculate even if some of the details of the data are lacking. Of all averages, it is affected least by fluctuations of sampling. It provides a good basis for comparison.
The demerits in using mean is It cannot be obtained by inspection nor located through a frequency graph. It cannot be in the study of qualitative phenomena not capable of numerical measurement i.e. Intelligence, beauty, honesty etc., It can ignore any single item only at the risk of losing its accuracy. It is affected very much by extreme values. It cannot be calculated for open-end classes. It may lead to fallacious conclusions, if the details of the data from which it is computed are not given.
MEDIAN The median is that value of the variants which divides the group into two equal parts, one part comprising all values greater, and the other, all values less than median. The Merits & demerits of Arithmetic median are Median is not influenced by extreme values because it is a positional average. Median can be calculated in case of distribution with open-end intervals. Median can be located even if the data are incomplete. Median can be located even for qualitative factors such as ability, honesty etc.
The demerits in using mean are a slight change in the series may bring drastic change in median value. In case of even number of items or continuous series, median is an estimated value other than any value in the series. It is not suitable for further mathematical treatment except its use in mean deviation. It is not taken into account all the observations.
The mode refers to that value in a distribution, which occur most frequently. It is an actual value, which has the highest concentration of items in and around it.
According toCowden The mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded at the most typical of a series of values. It is, thus, a positional measure. The Merits & demerits of mode is easy to calculate and in some cases it can be located mere inspection. Mode is not at all affected by extreme values. It can be calculated for open-end classes. It is usually an actual value of an important part of the series. In some circumstances it is the best representative of data.
The demerits in using mode is that its not based on all observations. It is not capable of further mathematical treatment. Mode is ill-defined generally; it is not possible to find mode in some cases. As compared with mean, mode is affected to a great extent, by sampling fluctuations. It is unsuitable in cases where relative importance of items has to be considered.
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