To calculate the five-number summary (minimum, Q1, median, Q3, maximum) from the given frequency table, we will follow these steps:

1. Organize the Data:

The frequency table is as follows:

Value	Frequency
3	1
5	2
6	2
7	1
8	3
10	3
11	1
12	2

From the frequency table, we can create a list of all data points by repeating the values according to their frequencies:

Data: $3, 5, 5, 6, 6, 7, 8, 8, 8, 10, 10, 10, 11, 12, 12$

2. Arrange the Data in Ascending Order:

The data is already in ascending order:

$3, 5, 5, 6, 6, 7, 8, 8, 8, 10, 10, 10, 11, 12, 12$

3. Find the Five-Number Summary:

1. Minimum (Smallest value):

The smallest value is 3.

2. Maximum (Largest value):

The largest value is 12.

3. Median (Q2):

The median is the middle value of the data. Since there are 15 values, the median is the 8th value:

$\text{Median} = 8$

4. First Quartile (Q1):

Q1 is the median of the first half of the data (values before the median). The first half of the data is:

$3, 5, 5, 6, 6, 7, 8$

Since there are 7 values in this subset, the median of these 7 values is the 4th value:

$Q1 = 6$

5. Third Quartile (Q3):

Q3 is the median of the second half of the data (values after the median). The second half of the data is:

$8, 8, 10, 10, 10, 11, 12, 12$

Since there are 8 values in this subset, the median of these 8 values is the average of the 4th and 5th values:

$Q3 = \frac{10 + 10}{2} = 10$

Five-Number Summary:

• Minimum = 3
• Q1 = 6
• Median (Q2) = 8
• Q3 = 10
• Maximum = 12

Would you like further details or explanations on any part of this? Let me know!

Here are 5 related questions:

1. How do you calculate the median for a set of data with an even number of values?
2. What is the interquartile range (IQR), and how is it calculated?
3. How do you interpret the five-number summary in a box plot?
4. What is the difference between Q1 and Q3 in a data set?
5. How does the five-number summary relate to the spread of the data?

Tip: A box plot is a great visual representation of the five-number summary, showing the spread and central tendency of the data.