Given the data:
5.6, 5.5, 5.1, 5.3, 5.2, 5.5, 5.6, 5.2, 5.7, 5.2
Let's draw a box plot using the given diameters.
A box plot has 5 number summary, which are:
Minimum, first quartile (Q1), median, thrid quartile(Q3), maximum.
It is represented below:
Hence, we have:
• Minimum: ,This is the smallest data value.
Therefore, the minimum is 5.1
• First Quartile (Q1):
The Q1 is the median of the lower half of the data.
Arrange the number s in ascending order:
5.1, 5.2, 5.2, 5.2, 5.3, 5.5, 5.5, 5.6, 5.6, 5.7
Lower half of data:
5.1, 5.2, 5.2, 5.2, 5.3
The median of the lower half is = 5.2
Therefore, the Q1 = 5.2
• Median:
Median is the middle data.
Arrange the number s in ascending order:
5.1, 5.2, 5.2, 5.2, 5.3, 5.5, 5.5, 5.6, 5.6, 5.7
The two middle numbers are:
5.3 and 5.5
SInce we have two middle numbers, the median will be the average of the two middle numbers.
[tex]\frac{5.3+5.5}{2}=\frac{10.8}{2}=5.4[/tex]
Therefore, the median is 5.4
• Third Quartile:
The Q3 is the median of the upper half of the data.
Arrange the number s in ascending order:
5.1, 5.2, 5.2, 5.2, 5.3, 5.5, 5.5, 5.6, 5.6, 5.7
Upper half of data:
5.5, 5.5, 5.6, 5.6, 5.7
Median of upper half = 5.6
Therefore, the third quartile, Q3 = 5.6
• Maximum:
The maximum is the greatest number in the data set.
The maximum is 5.7
Therefore, the five number summary is:
• Min = 5.1
,
• Q1 = 5.2
,
• Median = 5.4
,
• Q3 = 5.6
,
• Max = 5.7
Therefore, the box plot is below:
