To calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

Data (sorted):
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

1. Minimum:

The smallest value in the dataset is 3.5.

2. First Quartile (Q1):

Q1 is the median of the lower half of the data.
Lower half of the dataTo calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

Data (sorted):
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

1. Minimum:

The smallest value in the dataset is 3.5.

2. First Quartile (Q1):

Q1 is the median of the lower half of the data.
Lower half of the 3.5, 4, 4.6, 6, 6.8, 7.2
Median of the lower half: $(4.6 + 6)/2 = 5.3$

So, Q1 = 5.3.

3. Median:

The median is the middle value of the entire dataset.
Middle value: $7.2$ (since it's the 7th value in the sorted list).

So, Median = 7.2.

4. Third Quartile (Q3):

Q3 is the median of the upper half of the data.
Upper half of the dataTo calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

Data (sorted):
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

1. Minimum:

The smallest value in the dataset is 3.5.

2. First Quartile (Q1):

Q1 is the median of the lower half of the data.
Lower half of the 3.5, 4, 4.6, 6, 6.8, 7.2
Median of the lower half: $(4.6 + 6)/2 = 5.3$

So, Q1 = 5.3.

3. Median:

The median is the middle value of the entire dataset.
Middle value: $7.2$ (since it's the 7th value in the sorted list).

So, Median = 7.2.

4. Third Quartile (Q3):

Q3 is the median of the upper half of the data.
Upper half of the 7.5, 8, 8, 9, 10, 11
Median of the upper half: $(8 + 9)/2 = 8.5$

So, Q3 = 8.5.

5. Maximum:

The largest value in the dataset is 11.

Five-Number Summary:

• Minimum = 3.5
• Q1 = 5.3
• Median = 7.2
• Q3 = 8.5
• Maximum = 11

Would you like more details on this or any further questions?

Related Questions:

1. How is the interquartile range (IQR) calculated from the five-number summary?
2. What does each component of the five-number summary represent in real-world contexts?
3. How do outliers affect the five-number summary?
4. How can the five-number summary be used to construct a box plot?
5. How can you calculate the mean and standard deviation of the same dataset?

Tip: The interquartile range (IQR) is a measure of the spread of the middle 50% of the data and is found by subtracting Q1 from Q3.