Data Collection, Processing and Analysis Merits of the Arithmetic Mean, Latitudinal Extent of the Mainland of India Part 4
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Merits of the Arithmetic Mean

It is easy to understand the complete idea of the distribution and simple to workout.

It is the average of the values in a distribution. Hence, it has a balancing property in case of sample surveys.

It is widely used in case of normal distributions.
The arithmetic mean has certain limitations. It is affected by the extreme values especially when they are large. For example, income variations are very wide in case of Indian population.
Median: Median is the middle most positional average. It is worked out by arranging data in an ascending or descending order. For example, the value of the median is worked out by adding 1 to the number of observation and the sum divided by two. It is expressed as:
For example, if we are interested in working out the median latitude and longitude for the country, we must arrange these distributions in a tabular form.
Latitudinal Extent of the Mainland of India (8°4’ N to 37°6’ N)
9  10  11  12  13  14  15  16  17  18 
19  20  21  22  23  24  25  26  27  28 
29  30  31  32  33  34  35  36  37 
The median or middle most latitude of India is 23°N which is close to the Tropic of cancer (23°30’N). Since mainland of India starts from 8^{o}4’N which is a part of 9^{th} latitude and extends up to N which covers the latitude completely, hence the latitudinal coverage of India is approximately 29° latitudes. The median latitude is therefore, 23°N i.e.
8° + 15° = 23°N
Or, 8^{o }(Southern tip of India) + 15° (median value) = 23° (Middle East latitude of India). Similarly, we can also workout the median value for the longitudinal extent of India. The Longitudinal Extent of India ranges between = 68°7’ E to 97°25’E.
The median or middle most longitude for the country is 83°E.
69  70  71  72  73  74  75  76  77  78 
79  80  81  82  83  84  85  86  87  88 
89  90  91  92  93  94  95  96  97 
Longitudes are used to calculate local time, standard time of a nation, and international time which is linked to Greenwich Mean Time (GMT). Indian Standard Time is calculated keeping 82^{o}30’E longitude as the base. The median longitude for the country is 83^{o}E which is close to the standard meridian used for Indian Standard Time calculation.
Merits of Median

Being the middle most value, median remains unaffected by the extreme values in the distribution as in the case of arithmetic mean.

It is a partition value which divides the series into two nearly equal parts and remains the centre of gravity.

However, it cannot be worked out without putting data in an ascending or descending order. If data are large, it might be a time consuming and tedious job. The values of median will be erratic if one or two items are added or subtracted from the series.
Mode: It is one of the important measures of central tendency. The maximum concentration of items occurring in a distribution is considered to ascertain the mode. The value which occurs most frequently is identified as mode in case of ungrouped data. Similarly, for grouped data the mode can be calculated by identifying the class with the highest frequency. The mode denotes the centrality of the occurrence of an item in the distribution. The distribution of rural settlements in Uttar Pradesh is given below. Workout the mode for the data.
Distribution of Rural settlements in Uttar Pradesh 2001
Size of Rural Settlements  Very Small (Below 500 Population)  Small (500999)  Medium (15001999)  Large (20004999)  Very Large (5000 and above) 
Proportion of Distribution  16.69  23.46  47.97  10.59  1.29 
Solution: Arrange the data in a sequence (either from small to large or from large to small). Put up the frequency values against each. Now compare the frequencies. The distribution registering maximum frequency is identified as ‘mode’.