can you please explain how you arrived at your answer using the formulas/theory?

Question

can you please explain how you arrived at your answer using the formulas/theory? thank you very much

4) Which of the following statements are true? a) For symmetrical distributed data the mean, the median and the mode are equal to each other. b) The range of a set of numbers is usually about three times the standard deviation. c) If the set of number are skewed to the right and their histogram is unimodal then the mean is larger than the median d) If the numbers in a data set are all equal, then the variance and the standard are both zero.

Explanation / Answer

a) false as being symmetrical ; left and rigth hand values are equal ; mean and median will coincide but mode can vary; this is possible only when it is unimodal symmetric

b)false ; it is approximately 4 times.

c)true ; as skewness =(mean-mode)/std deviation; for skewness to the right means it is positve hence

mean -median>0

mean >median

d)true ; cause there is no deviation; and therefore they both should be 0

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