The five-number summary consists of the following five statistics:

1. Minimum: The smallest number in the data set.
2. First Quartile (Q1): The median of the lower half of the data.
3. Median (Q2): The middle value of the data.
4. Third Quartile (Q3): The median of the upper half of the data.
5. Maximum: The largest number in the data set.

Let’s find the five-number summary for the given data set:

58, 48, 50, 41, 56, 48, 65, 55, 69, 44, 61, 44, 55, 62, 52.

Step 1: Arrange the data in ascending order.

41, 44, 44, 48, 48, 50, 52, 55, 55, 56, 58, 61, 62, 65, 69.

Step 2: Identify the minimum and maximum.

• Minimum: 41
• Maximum: 69

Step 3: Find the median (Q2).

Since there are 15 data points, the median is the 8th value.

• Median (Q2): 55

Step 4: Find the first quartile (Q1).

The lower half of the data (before the median) is: 41, 44, 44, 48, 48, 50, 52. The median of this subset is the 4th value.

• First Quartile (Q1): 48

Step 5: Find the third quartile (Q3).

The upper half of the data (after the median) is: 55, 56, 58, 61, 62, 65, 69. The median of this subset is the 4th value.

• Third Quartile (Q3): 61

Final Five-Number Summary:

• Minimum: 41
• Q1: 48
• Median (Q2): 55
• Q3: 61
• Maximum: 69

Would you like more details on this process or have any other questions?

Related Questions:

1. How do quartiles help describe a data set?
2. How is the interquartile range (IQR) calculated from the five-number summary?
3. Can the five-number summary be used to detect outliers?
4. What is the difference between mean and median in data analysis?
5. How do you interpret box plots based on the five-number summary?

Tip: The five-number summary is especially useful for identifying the spread and distribution of data, helping to visualize variability.