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.
Similar Questions
The Standard Normal Distribution has mean equal to
Important Questions from Statistics
- Match the LIST-I with LIST-II
LIST-I LIST-II A. Sampling error I. Values that describe the characteristics of a population B. Parameters II. The standard deviation of the sampling distribution C. Sampling fraction III. Variation among sample statistics due to change D. Standard error IV. Proportion of the population contained in a sample
Choose the correct answer from the options given below: Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
Match List - I with List - II.
List - I List - II A. Sample proportion P = x/n I. $\frac{\sigma}{\sqrt{n}}$ B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ II. $\sigma^2 \sqrt{\frac{2}{n}}$ C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$
Choose the correct answer from the options given below :- The measurement or determinations of length, height, weight, volume, area, pressure etc. comes under:
- Which of the following options explain what a 'mean' assumes ?
(i) an interval level of measurement
(ii) a nominal level of measurement
(iii) an ordinal level of measurement
(iv) a ratio level of measurement
