Question

Find the five number summary for the data set shown below.

5, 3, 2, 8, 1, 5, 6, 13



Minimum:

Q1 (Quartile 1):

Median (Q2):

Q3 (Quartile 3):

Maximum:

Answer 1

Min: 1

Q1: 2.5

Q2: 5

Q3: 7

Maximum: 13

Answer 2

Answers:

• Min = 1
• Q1 = 2.5
• Median = 5
• Q3 = 7
• Max = 13

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How to find those answers:

The first step is to sort the data from smallest to largest.

Here is what it looks like after sorting:

1, 2, 3, 5, 5, 6, 8, 13

The middle most items are those two copies of '5'. It's a tie between them.

The midpoint is (5+5)/2 = 10/2 = 5

Therefore, the median or Q2 is 5

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Next we split the data into two groups

L = {1,2,3,5} = lower set of first four items

U = {5,6,8,13} = upper set of last four items

Find the median of set L to get (2+3)/2 = 5/2 = 2.5

Then find the median of set U to get (6+8)/2 = 14/2 = 7

These medians of the subsets mentioned are the values of Q1 and Q3 respectively

Q1 = 2.5

Q3 = 7

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Lastly the min and max are the smallest and largest items.

In this case 1 is the smallest and 13 is the largest

min = 1

max = 13