Question

Here is a set of sample data.

3	87	7	57	15	90	25	55	68	70
89	20	26	93	9	5	86	23	37	52
96	4	91

Base on the data above, identify the 5 number summary
_ , _ ,_ , _ , _

Answer 1

Before solving the given problem let us know a bit about Five Number Summary.

What is Five Number Summary?

A five number summary consists of,

• The Minimum Value
• The First Quartile
• The Second Quartile (i.e. the median)
• The Third Quartile
• The Maximum Value

The Minimum Value

The minimum value is the minimum value of the data set.

Quartiles

The p-th order quartile is a value such that p proportion of values are less than or equal to it and (1-p) proportion of values are greater than or equal to it. To find quartiles we first arrange the data in ascending or descending order.

First Quartile (Q₁)

Here p=1/4=0.25

where [n/4] is a box function.

Example: [1.2]=1, [1.9]=1, [2.6]=2

Second Quartile (Q₂)

Here p=1/2=0.5. The second quartile is also called the median.

Third Quartile (Q₃)

Here p=3/4=0.75

The Maximum Value

The maximum value is the maximum value of the data set.

Coming back to our problem,

Let us first arrange our data in ascending order,

Original Data

No.	Data
1	3
2	87
3	7
4	57
5	15
6	90
7	25
8	55
9	68
10	70
11	89
12	20
13	26
14	93
15	9
16	5
17	86
18	23
19	37
20	52
21	96
22	4
23	91

Data in ascending order

No.	Data
1	3
2	4
3	5
4	7
5	9
6	15
7	20
8	23
9	25
10	26
11	37
12	52
13	55
14	57
15	68
16	70
17	86
18	87
19	89
20	90
21	91
22	93
23	96

From here we can clearly see that the minimum value is 3 and the maximum value is 96.

Here n=23

First Quartile

Looking at the ascending data set,

Second Quartile

Looking at the ascending data set,

Third Quartile

Looking at the ascending data set,

Hence the five number summary is,

• The Minimum Value=3
• The First Quartile=15
• The Second Quartile=52
• The Third Quartile=87
• The Maximum Value=96