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The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44. The smallest and largest observations are 0 and 63. So the five-number summary would be 0, 0.5, 7.5, 44, 63.
A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. [1]: 378
For the data in this table the interquartile range is IQR = Q 3 − Q 1 = 119 ... maximum, and the first and third quartile constitute the Five-number summary. [9 ...
They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot. The minimum and the maximum value are the first and last order statistics (often denoted X (1) and X (n) respectively, for a sample size of n).
A box plot of the data set can be generated by first calculating five relevant values of this data set: minimum, maximum, median (Q 2), first quartile (Q 1), and third quartile (Q 3). The minimum is the smallest number of the data set. In this case, the minimum recorded day temperature is 57°F. The maximum is the largest number of the data set.
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This single number describes the general performance of a student across the range of their course experiences. [6] The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of statistics appeared.