Question

Please help!! Determine the five-number summary for the data set. 20, 26, 18, 31, 22, 28, 30

Answer 1

Answer:

• min = 18
• Q1 = 20
• median = 26
• Q3 = 30
• max = 31

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Explanation:

The first task is to sort the items given.

The sorted set is {18, 20, 22, 26, 28, 30, 31}

There are 7 values in that set. The median is going to be in slot 4 because n/2 = 7/2 = 3.5 rounds to 4.

The value in slot 4 is 26, meaning the median is 26.

There are 3 values below the median, and 3 values above it.

L = lower set = items below the median

L = {18,20,22}

U = upper set = items above the median

U = {28,30,31}

The median of set L is 20, showing that Q1 = 20 is the first quartile.

The median of set U is 30, meaning Q3 = 30 is the third quartile.

The min and max are exactly what they sound like: they are the smallest and largest items. In this case, we have min = 18 and max = 31.