Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70. (a) what is the mean of the data? What is the median? (b) what is the mode of the data? Comment on the data's modality (i.E., bimodal, trimodal, etc.). (c) what is the midrange of the data? (d) can you find (roughly) the first quartile (q1) and the third quartile (q3) of the data? (e) give the five-number summary of the data. (f) show a boxplot of the data. (g) how is a quantile-quantile plot di ff erent from a quantile plot?
Answers
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a) The (arithmetic) mean of the data is: = 809/27 = 30.
The median (middle value of the ordered set, as the number of values in the set is odd) of the data is: 25.
b) This data set has two values that occur with the same highest frequency.
The modes (values occurring with the greatest frequency) of the data are 25 and 35.
c) The mid range (average of the largest and smallest values in the data set) of the data is: (70+13)=2 = 41.5
d) The first quartile (corresponding to the 25th percentile) of the data is: 20. The third quartile (corresponding to the 75th percentile) of the data is: 35.
e) third quartile, and maximum value. It provides a good summary of the shape of the distribution and for this data is: 13, 20, 25, 35, 70.
f) use the graph to show this data.
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