Five-Number Summary is a statistical summary that describes the distribution of a dataset using five key values: the minimum, first quartile, median, third quartile, and maximum.
Question 1: What is the minimum value in the given data: 10, 20, 5, 15, 25, 30?
Solution:
Step 1: Arrange the data in ascending order:
5, 8, 10, 15, 20, 25, 30
Step 2: The first value in the sorted data is the minimum value.
Minimum Value = 5
Question 2: What is the maximum value in the given data set: 10, 20, 5, 15, 25, 30?
Solution:
Step 1: Arrange the data in ascending order:
5, 8, 10, 15, 20, 25, 30
Step 2: The last value in the sorted data is the maximum value.
Maximum Value = 30
Question 3: What is the median value in the given data: 10, 20, 5, 15, 25, 30, 8 ?
Solution:
Step 1: Arrange the data in ascending order:
5, 8, 10, 15, 20, 25, 30
Step 2: Find the median using the formula:
Median Position = (n + 1) / 2
Here, n = 7
Median Position = (7 + 1) / 2 = 8 / 2 = 4
So, the median is the 4th term in the sorted data.
Median Value = 15
Question 4: Find the 5-number summary for the given data: 10, 20, 5, 15, 25, 30, 8 ?
Solution:
Step 1: Arrange the data in ascending order:
5, 8, 10, 15, 20, 25, 30
Step 2: Find the Minimum, Median, and Maximum values.
- Minimum Value = 5
- Median Value = 15
- Maximum Value = 30
Step 3: Find the First Quartile (Q1).
Q1 Position = (n + 1) / 4
= (7 + 1) / 4
= 8 / 4
= 2
So, Q1 is the 2nd term in the sorted data.
Q1 = 8
Step 4: Find the Third Quartile (Q3).
Q3 Position = 3(n + 1) / 4
= 3(7 + 1) / 4
= 3 Ã 8 / 4
= 24 / 4
= 6
So, Q3 is the 6th term in the sorted data.
Q3 = 25
Question 5: Find out the 5-number summary for the data 1, 10, 5, 15, 2, 12, 4, 14 ?
Solution:
Step 1: Arrange the data in ascending order:
1, 2, 4, 5, 10, 12, 14, 15
Step 2: Find the Minimum and Maximum values.
- Minimum Value = 1
- Maximum Value = 15
Step 3: Find the Median (Q2).
Median Position = (n + 1) / 2
= (8 + 1) / 2
= 9 / 2
= 4.5
Since the position is 4.5, take the average of the 4th and 5th terms.
Median = (5 + 10) / 2
= 15 / 2
= 7.5
Median (Q2) = 7.5
Step 4: Find the First Quartile (Q1).
Q1 Position = (n + 1) / 4
= (8 + 1) / 4
= 9 / 4
= 2.25
Take the average of the 2nd and 3rd terms.
Q1 = (2 + 4) / 2
= 6 / 2
= 3
Q1 = 3
Step 5: Find the Third Quartile (Q3).
Q3 Position = 3(n + 1) / 4
= 3(8 + 1) / 4
= 27 / 4
= 6.75
Take the average of the 6th and 7th terms.
Q3 = (12 + 14) / 2
= 26 / 2
= 13
Q3 = 13
