J Pharmacol Pharmacother. 2011 Jul-Sep; 2(3): 214–215. Apart from the mean, median and mode are the two commonly used measures of central tendency. The median is sometimes referred to as a measure of location as it tells us where the data
are.[1] This article describes about median, mode, and also the guidelines for selecting the appropriate measure of central tendency. Median is the value which occupies the middle position when all the observations are arranged in an ascending/descending order. It divides the frequency distribution exactly into two halves.
Fifty percent of observations in a distribution have scores at or below the median. Hence median is the 50th percentile.[2] Median is also known as ‘positional average’.[3] It is easy to calculate the median. If the number of observations are odd, then (n + 1)/2th
observation (in the ordered set) is the median. When the total number of observations are even, it is given by the mean of n/2th and (n/2 + 1)th observation.[2] It is easy to compute and comprehend. It is not distorted by outliers/skewed
data.[4] It can be determined for ratio, interval, and ordinal scale. Disadvantages
MODEMode is defined as the value that occurs most frequently in the data. Some data sets do not have a mode because each value occurs only once. On the other hand, some data sets can have more than one mode. This happens when the data set has two or more values of equal frequency which is greater than that of any other value. Mode is rarely used as a summary statistic except to describe a bimodal distribution. In a bimodal distribution, the taller peak is called the major mode and the shorter one is the minor mode. Advantages
Disadvantages
POSITION OF MEASURES OF CENTRAL TENDENCYThe relative position of the three measures of central tendency (mean, median, and mode) depends on the shape of the distribution. All three measures are identical in a normal distribution [Figure 1a]. As mean is always pulled toward the extreme observations, the mean is shifted to the tail in a skewed distribution [Figure 1b and c]. Mode is the most frequently occurring score and hence it lies in the hump of the skewed distribution. Median lies in between the mean and the mode in a skewed distribution.[6,7] The relative position of the various measures of central tendency. (a) Normal distribution (b) Positively (right) skewed distribution (c) Negatively (left) skewed distribution SELECTING THE APPROPRIATE MEASUREMean is generally considered the best measure of central tendency and the most frequently used one. However, there are some situations where the other measures of central tendency are preferred. Median is preferred to mean[3] when
FootnotesSource of Support: Nil Conflict of Interest: None declared. REFERENCES1. Swinscow TD, Campbell MJ. 10th ed(Indian) New Delhi: Viva Books Private Limited; 2003. Statistics at square one. [Google Scholar] 2. Gravetter FJ, Wallnau LB. 5th ed. Belmont: Wadsworth – Thomson Learning; 2000. Statistics for the behavioral sciences. [Google Scholar] 3. Sundaram KR, Dwivedi SN, Sreenivas V. 1st ed. New Delhi: B.I Publications Pvt Ltd; 2010. Medical statistics principles and methods. [Google Scholar] 4. Petrie A, Sabin C. 3rd ed. Oxford: Wiley-Blackwell; 2009. Medical statistics at a glance. [Google Scholar] 5. Norman GR, Streiner DL. 2nd ed. Hamilton: B.C. Decker Inc; 2000. Biostatistics the bare essentials. [Google Scholar] 6. SundarRao PS, Richard J. 4th ed. New Delhi: Prentice Hall of India Pvt Ltd; 2006. Introduction to biostatistics and research methods. [Google Scholar] 7. Glaser AN. 1st Indian Ed. New Delhi: Lippincott Williams and Wilkins; 2000. High Yield Biostatistics. [Google Scholar] 8. Dawson B, Trapp RG. 4th ed. New York: Mc-Graw Hill; 2004. Basic and Clinical Biostatistics. [Google Scholar] Articles from Journal of Pharmacology & Pharmacotherapeutics are provided here courtesy of Wolters Kluwer -- Medknow Publications Which of the following situations the best measure of central tendency to be used is the mean?The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average. For data from skewed distributions, the median is better than the mean because it isn't influenced by extremely large values.
When would you use median as a measure of central tendency?The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.
Why is median better than mean?When you have a symmetrical distribution for continuous data, the mean, median, and mode are equal. In this case, analysts tend to use the mean because it includes all of the data in the calculations. However, if you have a skewed distribution, the median is often the best measure of central tendency.
What is the most commonly used measure of central tendency?Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).
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