The sum of deviation taken from which of the descriptive statistical measures is always equal to zero?
Mean
To solve this question, we need to understand the concept of deviation and how it relates to different statistical measures. Let's explore the options:
- Mean: The sum of deviations from the mean is always zero. This is because the mean is defined as the average of all data points, ensuring that any excess is exactly balanced out by deficits. Mathematically, if \( x_1, x_2, ..., x_n \) are data points and \( \bar{x} \) is the mean, then: \[\sum (x_i - \bar{x}) = 0\] This property is a fundamental characteristic of the mean.
- Median: The median is the middle value of a dataset when it is ordered. The sum of deviations from the median is not always zero.
- Mode: The mode is the most frequently occurring value in a dataset. The sum of deviations from the mode does not guarantee a sum of zero as it depends on the distribution of the other values.
- Percentile: A percentile indicates the relative standing of a value in a dataset. Deviation from a particular percentile does not result in zero unless by coincidence.
Based on this reasoning, the correct answer is Mean, as it is the only measure for which the sum of deviations is always zero.
Hence, the correct option is Mean.
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