When summarizing interval-ratio variable data using descriptive statistics what

Question

When summarizing interval-ratio variable data using descriptive statistics what do we lose in our understanding of a sample of we just report the mean and not any measures of dispersion such as the interquartile range or standard deviation? How might this apply to our understanding of a variable such as crime rates in major cities or incarceration rates for minorities across countries? When summarizing interval-ratio variable data using descriptive statistics what do we lose in our understanding of a sample of we just report the mean and not any measures of dispersion such as the interquartile range or standard deviation? How might this apply to our understanding of a variable such as crime rates in major cities or incarceration rates for minorities across countries?

Explanation / Answer

Reporting only mean wil tell only what the center of distibution is , that is, where the values most likely to be found.

However, how dispersed these values around the center are is told by standard deviation/interquartile range which help us to know whether the centre value is truly representative of whole set of values or if there is large dispersion then it is not.

In case of crime rate in major cities we need to know how far the crime rates in various cities are from the average/mean which will tell us whether the crime rates are consistent in all cities or dispersed a lot.

Similarly standard deviation tells us how many times the minorites are imprisoned and whether there is consistency in impsrionment or not

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