We have the following sample data set:
4, 9, 16, 18, 21, 24, 29, 31, 35, 37, 43, 44, 49, 51, 52, 56, 58, 66, 68, 71, 90, 93, 95
We must identify the 5 number summary: (min, Q1, median, Q3, max).
1) The first step consists in ordering the data, from the smaller value to the bigger one. The list is already ordered:
4, 9, 16, 18, 21, 24, 29, 31, 35, 37, 43, 44, 49, 51, 52, 56, 58, 66, 68, 71, 90, 93, 95
2) From the order set of numbers we identify the min (the minimum value) and the max (the maximum value):
• min = 4
,
• max = 95
3) Counting the number of elements of the data set, we count 23 elements.
The median is the middle number in a sorted, ascending or descending, list of numbers.
Looking at the numbers of the list, we see that in the middle we have the number 44, so we have:
• median = 44
4) Quartiles are the values that divide a list of numbers into quarters. To find the quartiles we must divide the list into four equal parts. To do that first we divide the list into two equal parts, excluding the median:
• 4,9, 16, 18, 21, ,24,, 29, 31, 35, 37, 43
,
• 49, 51, 52, 56, 58, ,66,, 68, 71, 90, 93, 95
Now, we must divide each part into two equal parts. Each list has an odd number of elements, the elements in the middle of each list are the Q1 and Q3 quartiles, respectively. So we have:
• Q1 = 24
,
• Q3 = 66
Answer
The 5 number summary (min, Q1, median, Q3, max) are (4, 24, 44, 66, 95).
