| MEASURES OF CENTRAL TENDENCY |
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It is known that the
- numbers of DMFT
- age at the eruption of molars
- fluoride concentration in water
all vary from unit to unit or from place to place. |
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Hence there is a necessity of expressing the observations in a precise manner, preferably using a single estimate so that it summarizes the observations. |
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This also enables comparison of two or more data series. |
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For overall comparison of the distributions, the entire mass of data may be summarized using a single value. |
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This single estimate of a series of data that summarizes the data is known as the parameter and one such parameter is the measure of central tendency. |
| Objective |
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The main objective of measure of central tendency is
- To condense the entire mass of data and
- To facilitate compensation
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| Properties |
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A good measure of central tendency should satisfy the following properties |
| 1. |
It should be easy to understand and compute. |
| 2. |
It should be based on each and every item in the series. |
| 3. |
It should not be affected by extreme observations ( either too small or too large values ). |
| 4. |
It should be capable of further statistical computations. |
| 5. |
It should have sampling stability, i.e., if different samples of same size. Say 10 are picked up from the same population, and the measure of central tendency is calculated, they should not differ from each other markedly. |
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The most common measures of central tendency that are used in dental sciences are
- Arithmetic mean - mathematical estimate
- Median - positional estimate
- Mode - based on frequency
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| ARITHMETIC MEAN |
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It is the simplest measure of central tendency |
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when we have ungrouped data, mean is calculated as follows |
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Example |
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The number of decayed teeth in a group of 10 children aged 5 years are as follows |
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2 - 2 - 4 - 1 - 3 - 0 - 5 - 2 - 3 - 4 |
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Then the mean number of decayed teeth for this group is calculated as |
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Here |
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n = 10 |
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Σ X = 2 + 2 + 4 + 1 + 3 + 0 + 5 + 2 + 3 + 4 = 26 |
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When the number of observations are many the above method will be tedious and hence frequency distribution tables are formed and the mean is calculated from the table. |
| MEDIAN |
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The median, by definition, is the middle value in a distribution such that one half of the units in the distribution have a value smaller than or equal to the median and one half has a value higher than or equal to the median. |
| Calculation of Median |
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For ungrouped data, to calculate the median, all the observations are arranged in the order of their magnitude and then the middle value of the observations is selected as the median. |
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When the number of observations is odd the value will correspond to a single value |
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And when the number of observations is even, the mean of the two middle values may be taken as the median. |
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Example |
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The following are the number of visits to a dentist by 10 patients |
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13 - 8 - 4 - 3 - 4 - 2 - 8 - 1 - 7 - 4 . |
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For calculating the median, the number are first arranged in order of magnitude as |
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1 - 2 - 3 - 4 - 4 - 4 - 7 - 8 - 8 - 13 |
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Since their are ten patients, the average of 5th and 6th patient is calculated as the median, which is |
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4 + 4 = 8 / 2 = 4. |
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Thus it is seen that median is a positional average. It is not capable of future treatment. |
| MODE |
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The mode or the modal value is that value in a series of observations that occurs with the greatest frequency. |
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For example the mode of the series on "age at eruption of the canine" as |
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6 - 6 - 5 - 7 - 8 - 6 - 7 - 5 |
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would be 6. |
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There can be more than one mode for a series |
| conclusion |
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So, depending upon the
- nature of data, and
- objective of study
the appropriate measure of central tendency may be used. |
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