Best Central Tendency

Average or measure of central tendency is a single quantity which enables us to know the average character of the data under investigation. It is a single value which is the representative of all the items and which the mind can grasp simply and quickly. Average is the quantity around which the data tends to cluster or accurate. Under different types of situations, data tends to cluster on different individuals having different types of nature. Thus, under different types of situations a single type of average is unsuitable

Measures of best central tendency:

   Consequently, the following are the measure of central tendency which are commonly used:
 (i)     Arithmetic mean ( or simply mean / average)
 (ii)     Median.
 (iii)    Mode.
Each one of the central tendency is determined by differently, and the one of the measures of central tendency is best to utilize depends upon the situation of the given data.

Example for best central tendency:

Example 1:
    Measure the average, median and mode of the given employees income. The actual annual incomes of the 15 workers are shown below, and then measure the best central tendency?

$10,345	$11,453	$9,654
$12,469	$7,499	$14,354
$7,499	$8,346	$12,486
$6,678	$16,563	$11,123
$6,900	$17,523	$9,341

Solution:
The sorting order of the given employees incomes, are

$6,678	$6,900	$7,499	$7,499	$8,346
$9,341	$9,654	$10,345	$11,123	$11,453
$12,469	$12,486	$14,354	$16,563	$17,523

The mean of the profit is
      Mean = `($6,678 + $6,899 + ... + $16,563 + $ 17,523)/(15)`
               = $10,815.5
    Median = $10,345
    Mode = $7,499
    For this data, the mean is $10,815.5, the median is $10,345, and the mode is $7,499. Of these, the mean or median is the most representative.


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Example 2:
The following data to measure the best central tendency.
(a) 7, 20, 15, 11, 8, 3, 2, 0, 15
(b) 9, 8, 7, 6, 5, 6, 7, 8, 9
(c) 6, 1, 2, 3, 5, 5, 4, 3, 0
Solution:
(a) The mean of the central tendency is 4.23, the central tendency of median is 3, and the mode of the given data is 2. Therefore, the best central tendency of mode is most likely the most representative.
(b) The mean and median of central tendencies are all 5 and the two modes are 1 and 9 (the distribution is bimodal). Therefore, the mean or median of the central tendency is the most representative.
(c) Here, the mean = 4.59.
             the median  =  5.
         and the mode  =  1.
Therefore, the mean or median is the best central tendency.