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Q: For which measure of central tendency will the sum of the deviations always be zero?

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The mean.

If the distribution is positively skewed distribution, the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency. This is true if we assume the distribution has a single mode.

The sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.

You will need to find the middle number (mode) or all them could be.* * * * * If there are three modes then so be it. One of the problems with the mode, as a statistical measure is that there may not be any or there may be many. A mode had little to do with the middle number - other than the expectation that, thanks to a central tendency, many distributions are likely to be clustered around their middle. But this is not always the case.

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Related questions

For which measure of central tendency will the sum of the deviations always be zero?

yes is it the median?

mean

The mean.

the mean

Difference (deviation) from the mean.

If the distribution is positively skewed distribution, the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency. This is true if we assume the distribution has a single mode.

Its the one most commonly used but outliers can seriously distort the mean.

One of the characteristics of mean when measuring central tendency is that when there are positively skewed distributions, the mean is always greater than the median. Another characteristic is that when there are negatively skewed distributions, the mean is always less than the median.

The sum of total deviations about the mean is the total variance. * * * * * No it is not - that is the sum of their SQUARES. The sum of the deviations is always zero.

If the distribution is positively skewed , then the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency (If it is a uni-modal distribution). If the distribution is negatively skewed then mean will always be the lowest estimate of central tendency and the mode will be the highest estimate of central tendency. In both positive and negative skewed distribution the median will always be between the mean and the mode. If a distribution is less symmetrical and more skewed, you are better of using the median over the mean.

0 (zero).

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