Definition
Central tendency is a statistical measure that identifies a single value as representative of an entire dataset or distribution. This value depicts the center or typical behavior of the dataset. Common measures of central tendency include the mean, median, and mode.
Mean
The mean, or average, is the sum of all values divided by the number of values. It is typically used for quantitative data.
Median
The median is the middle value when all observations are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. It is useful in determining the typical value in skewed distributions.
Mode
The mode is the value or values that appear most frequently in a dataset. It can be used for both qualitative and quantitative data.
Examples
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Mean Example: Dataset: [1, 2, 3, 4, 5] Mean = (1+2+3+4+5)/5 = 3
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Median Example: Dataset: [1, 2, 3, 4, 5] Median = 3
Dataset: [1, 2, 3, 4, 5, 6] Median = (3+4)/2 = 3.5
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Mode Example: Dataset: [1, 2, 2, 3, 4] Mode = 2
Frequently Asked Questions
Q: When should I use the median over the mean? A: The median is preferred when the data is skewed or contains outliers, as it is not affected by extremely high or low values like the mean.
Q: Can a dataset have more than one mode? A: Yes, a dataset can have more than one mode if multiple values appear with the same highest frequency. Such datasets are called bimodal or multimodal.
Q: What are the limitations of using central tendency measures? A: Measures of central tendency do not provide information about the spread or distribution of values around the central point. Complementing them with measures of variability such as range, variance, and standard deviation is crucial.
Related Terms
Standard Deviation: A measure of the amount of variation or dispersion in a set of values.
Range: The difference between the maximum and minimum values in a dataset.
Variance: The expectation of the squared deviation of a random variable from its mean, giving a measure of the spread.
Skewness: A measure of the asymmetry of the probability distribution of a real-valued random variable.
Online References
Suggested Books for Further Studies
- “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne.
- “Introduction to the Practice of Statistics” by David S. Moore, George P. McCabe, and Bruce A. Craig.
- “The Essentials of Statistics” by Mario Triola.
Fundamentals of Central Tendency: Statistics Basics Quiz
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