Calculate the five numbers summary of The Steve data set 5 6 6 7 7 8 8 9 9 14 16 which of the following choices is quartile 3 2.5 8 9 6.5

Answer 1

To calculate the five-number summary of the given data set: 5, 6, 6, 7, 7, 8, 8, 9, 9, 14, 16, we need to find:

1. Minimum
2. First Quartile (Q1)
3. Median (Q2)
4. Third Quartile (Q3)
5. Maximum

Step 1: Organization

The data is already sorted in ascending order: \[ 5, 6, 6, 7, 7, 8, 8, 9, 9, 14, 16 \]

Step 2: Find Minimum and Maximum

• Minimum: 5
• Maximum: 16

Step 3: Find Median (Q2)

The median (Q2) is the middle value. With 11 values, the median is the value in the 6th position (since there are 11 numbers): \[ Q2 = 8 \]

Step 4: Find Q1 and Q3

To find Q1, we look at the first half of the data set (values below the median): \[ 5, 6, 6, 7, 7 \]

Q1 is the median of this subset. Since there are 5 numbers, the median is the 3rd value: \[ Q1 = 6 \]

For Q3, we look at the second half of the data set (values above the median): \[ 8, 9, 9, 14, 16 \]

Q3 is the median of this subset. Since there are 5 numbers, the median is the 3rd value: \[ Q3 = 9 \]

Step 5: Summary of the five-number summary

1. Minimum: 5
2. Q1: 6
3. Median (Q2): 8
4. Q3: 9
5. Maximum: 16

Conclusion

Among the choices provided (2.5, 8, 9, 6.5), the value for Q3 is: 9.