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If two distributions have exactly the same mean and standard deviation must their histograms have the same shape If they have the same five-number summary must their histograms have the same shape?
No, and no. Think about two skewed distributions that are mirrored across the mean so that one is right and one is left. they have the same mean and standard deviation, but are opposite. Also, the 5 number summary does not affect a histogram
Multiple values for the same set of numbers mean median or mode?
Any set of numbers can have only one mean and only one median but it can have as many modes as it has values.
What will be the sampling distribution of the mean for a sample size of one?
It will be the same as the distribution of the random variable itself.
What is standard deviation of the mean?
If repeated samples are taken from a population, then they will not have the same mean each time. The mean itself will have some distribution. This will have the same mean as the population mean and the standard deviation of this statistic is the standard deviation of the mean.
Are average and range the same thing?
No, they are not the same thing. Mean and average are the same thing.
