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Q: Is the best measure of central tendency always the mean?

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The mean cannot be used with ordinal data. The best measure of central tendency for ordinal data is usually the median. A common example of ordinal data is the scale you see in many surveys. 1=Strongly disagree; 2=Disagree; 3=Neutral; 4=Agree; 5=Strongly agree. The mean would have not meaning here ( no pun intended) The median is simple the middle value. The mode does have meaning.

ANS: Measures of central tendency will quantify the middle of the distribution. The measures in case of population are the parameters and in case of sample, the measures are statistics that are estimates of population parameters. The three most common ways of measuring the centre of distribution is the mean, mode and median.In case of population, the measures of dispersion are used to quantify the spread of the distribution. Range, interquartile range, mean absolute deviation and standard deviation are four measures to calculate the dispersion.The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features.i. With respect to nature of data to cluster around a central valueii. With respect to their spread from their central valueArithmetic mean is defined as the sum of all values divided by number of values.Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.Mode is the value which has the highest frequencyThe measures of variations are:i. Range (R)ii. Quartile Deviations ( Q.D)iii. Mean Deviations (M.D)iv. Standard Deviations (S.D)Coefficient of variation is a relative measure expressed in percentage and is defined as:CV in %=

It depends on what you want. If it is simply to know what the "average" value is, then the mode may be the best in these circumstances. But if you want to do anything else - eg determine the spread of the data, or test any hypothesis about the data, you will be much better off with the mean. That is because the mean has been studied much more comprehensively than other measures of central tendency and its characteristics are incorporated into many statistical tests.

Answer with an exampleIf you have a data series like: 1,2,2,3 What is the mean, median and mode of this thing:Mean= 2Median = 2Mode = 2Now if you have 1,2,2,3,1000Then we gotta have three measures asMode remains = 2Median shifts slightly toward threeMean becomes 201.6So you can see that three measures are required to capture the tendency of a data set in a more complete fashion.Although the mean does have this problem of being distorted by outliers (extreme values), it is the best measure of central tendency if more sophisticated analyses are required. This is because the properties of the mean, itself, are better understood. This means there is a wide range of powerful statistical techniques that can be applied to data using the mean.

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Related questions

mean

Median

The mode.

mean

you need to be more specific with your question!!

The median.

by getting the mean and multiply by the median

The mode.

never * * * * * When the data are qualitative. The mean and median are unusable in such cases and the mode is the only sensible measure.

The mean may be a good measure but not if the data distribution is very skewed.

The median, as long as you don't want to do any serious statistical testing.

The arithmatic mean is not a best measure for central tendency.. It is because any outliers in the dataset would affect its value thus it is considered not a robust measure.. The mode or median however would be better to measure central tendency since outliers wont affect it value.. Consider this example : Arithmatic mean dan mode from 1, 5, 5, 9 is 5.. If we add 30 to the dataset then the arithmatic mean will be 10 but the mode will still same.. Mode is more robust than arithmatic mean..

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