The following data are numerical statistics for five data sets. Using Excel\'s s

Question

The following data are numerical statistics for five data sets. Using Excel's statistical function, complete the following questions.

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a. Compare the data sets with regard to measures of central tendency. Does the mean equal the median for each data set? What does it mean if they are equal? Comment on each data set.

b. Are any data sets similar? Do some data sets appear simliar with regard to measures of central tendency but different with regard to measures of dispersion? Comment on each data set.

DATA SET MEAN MEDIAN RANGE SD 1 50 50 6 2 2 70 100 100 47 3 25 15 92 25 4 50 44.5 60 22 5 33 0 100

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Explanation / Answer

(a) The measures of central tendency used are mean and median.
If mean is equal to the median, it means that the underlying distribution of the data set is symmetric.
For data set 1, mean is equal to median. This means the data set is symmetric.
For data set 2, mean is less than the median. This means that the data set is negatively skewed.
For data sets 3, 4 and 5, mean is greater than the median. This means that the data sets are positively skewed.

(b) No, none of the 5 data sets are similar in terms of measures of central tendency or dispersion.
Data set 1 and 4 have equal means but data set 1 has less SD and range than data set 4. This indicates that the variation in data set 1 is lesser than that in the case of data set 4.
Data sets 2, 3 and 5 are not similar with any other data sets in terms of equal measures of central tendency and different measures of dispersion.
Also, data sets 2 and 5 have equal values of range.

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