The 10 hypothetical numbers which meets the conditions given on the question may include :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary include the maximum, minimum, lower quartile, Median and upper quartile of a distribution.
The five number summary of the hypothetical data are:
Median: 6
Minimum: 1
Maximum: 12
Lower quartile: 2.75
Upper quartile: 10
Comparing the 5 - number summary of the hypothetical data with that of the given boxplot.
From the given boxplot shown :
Minimum value = 1
Maximum value = 12
Median = 6
LOWER QUARTILE, Q1 = 4
UPPER QUARTILE, Q3 = 8
IQR = (Q3 - Q1) = 8 - 4 = 4
THE 10 made up numbers :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary for the made up data :
Median = 1/2(n+1)th term = 5.5th term = (6+6)/2 = 6
Minimum: 1
Maximum: 12
First quartile = 1/4(n+1)th = 2.75th term = (2+3)/2 = 2.5
Third quartile: 3/4(n+1)th term = 8.25 = (10+10)/2 = 10
Interquartile Range: (10 - 2.5) = 7.5
- The original data values and hypothetical data have the same minimum and maximum and median values.
- The hypothetical data has an higher IQR value than the original data.
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