Measures of central tendency refer to single values that describe a given set of data by presenting the central position within the data ( Manikandan, 2011). The values include the mean, mode and median and there are used under different conditions. The tables below illustrate the mean, median, and mode of the data in each group.
Mean
|
Groups |
Mean |
| 7, 4, 18, 6, 21, 35, 7, 12, 1, 4 |
11.5 |
| 5, 8, 45, 25, 78, 1, 34, 56, 78 |
36.7 |
| 23, 45, 67, 89, 12, 32, 54, 78 |
50 |
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Median
|
Groups |
Median |
| 7, 4, 18, 6, 21, 35, 7, 12, 1, 4 |
7 |
| 5, 8, 45, 25, 78, 1, 34, 56, 78 |
34 |
| 23, 45, 67, 89, 12, 32, 54, 78 |
49.5 |
Mode
|
Groups |
Mode |
| 7, 4, 18, 6, 21, 35, 7, 12, 1, 4 |
4 & 7 |
| 5, 8, 45, 25, 78, 1, 34, 56, 78 |
78 |
| 23, 45, 67, 89, 12, 32, 54, 78 |
No mode |
For the first group of data, the mean is determined by adding the total values and dividing the result with the number of individual values (Wilcox & Keselman, 2003). Obtaining the mean of the data group is the same as obtaining the average of the data group. For the median group, the median is realized by re-arranging the data in an ascending manner (i.e. from lowest to highest) and identifying the middle number (Deshpande, Gogtay & Thatte, 2016). When the median constitutes of two digits, one is required to find the average of both numbers. The mode is obtained by identifying the most appearing number in a set of data (Bickel, 2003). However, if values appear at the same rate, both are considered as being the mode of the group. Additionally, if no data appears more than once in a data set, the data set is said to have no mode.
References
Bickel, D. R. (2003). Robust and efficient estimation of the mode of continuous data: the mode as a viable measure of central tendency. Journal of statistical computation and simulation, 73(12), 899-912.
Deshpande, S., Gogtay, N. J., & Thatte, U. M. (2016). Measures of central tendency and dispersion. Journal of the Association of Physicians of India, 64, 64-66.
Manikandan, S. (2011). Measures of central tendency: Median and mode. Journal of pharmacology and pharmacotherapeutics, 2(3), 214.
Wilcox, R. R., & Keselman, H. J. (2003). Modern robust data analysis methods: measures of central tendency. Psychological methods, 8(3), 254.
