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my data of patient satisfaction is based on a rating their experience on a scale 0-10...

my data of patient satisfaction is based on a rating their experience on a scale 0-10 however this then accumulated as average percentage statistic. so is the data considered quantitative continuous or discrete? and why

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It is a continuous variable.

This is because the accumulated ( or aggregated ) number can hold any value between 0 to 10 , even decimals and is therefore not discrete.

Hence, the average percentage statistic is a CONTINUOUS variable and not discrete

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