Five-number summary for this data set is,
min = 12, Q1 =14, median = 15 , Q3 = 18, max = 19 .
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Consider the given data set, {12, 14, 15, 14, 16, 18, 19, 18}.
The five-number summary for this data set consists of min, Q1, median, Q3, and max.
First to arrange the data set in ascending order,
{12, 14, 14, 15, 16, 18, 18, 19).
Maximum value = 19, minimum value = 12
The total observations are 8.
So , Median = Mean of middle most terms
Middle most terms are 14, 16
Median = (14 + 16) / 2 = 30 / 2 = 15
Now to find first quartile (Q1) = Median of first half {12, 14, 14, 15}
Q1 = (14 + 14) / 2 = 28 / 2 = 14
Now to find third quartile (Q3) = Median of second half {16, 18, 18, 19}
Q3 = (18 + 18) / 2 = 36 / 2 = 18
Therefore, five-number summary for this data set is,
min = 12, Q1 =14, median = 15 , Q3 = 18, max = 19 .
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