Which measure of central tendency should be used to most accurately describe the data above?
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A descriptive summary of a dataset through a single value that reflects the center of the data distribution Show What is Central Tendency?Central tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. Along with the variability (dispersion) of a dataset, central tendency is a branch of descriptive statistics. The central tendency is one of the most quintessential concepts in statistics. Although it does not provide information regarding the individual values in the dataset, it delivers a comprehensive summary of the whole dataset. Measures of Central TendencyGenerally, the central tendency of a dataset can be described using the following measures:
Even though the measures above are the most commonly used to define central tendency, there are some other measures, including, but not limited to, geometric mean, harmonic mean, midrange, and geometric median. The selection of a central tendency measure depends on the properties of a dataset. For instance, the mode is the only central tendency measure for categorical data, while a median works best with ordinal data. Although the mean is regarded as the best measure of central tendency for quantitative data, that is not always the case. For example, the mean may not work well with quantitative datasets that contain extremely large or extremely small values. The extreme values may distort the mean. Thus, you may consider other measures. The measures of central tendency can be found using a formula or definition. Also, they can be identified using a frequency distribution graph. Note that for datasets that follow a normal distribution, the mean, median, and mode are located on the same spot on the graph. Related ReadingsThank you for reading CFI’s guide on Central Tendency. To keep learning and advancing your career, the following resources will be helpful:
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] Advantages
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 |
