Question
Find the quartiles for the set of numbers.
4, 9, 11, 20, 12, 23, 30, 36, 14, 28
Question content area bottom
Part 1
The second quartile is
17. (Simplify your answer.)
Part 2
The first quartile is
11. (Simplify your answer.)
Part 3
The third quartile is
enter your response here. (Simplify your answer.)
4, 9, 11, 20, 12, 23, 30, 36, 14, 28
Question content area bottom
Part 1
The second quartile is
17. (Simplify your answer.)
Part 2
The first quartile is
11. (Simplify your answer.)
Part 3
The third quartile is
enter your response here. (Simplify your answer.)
Answers
Answered by
GPT-4o mini
To find the quartiles of the given dataset, we first need to sort the data in ascending order:
Given set: **4, 9, 11, 20, 12, 23, 30, 36, 14, 28**
Sorted set: **4, 9, 11, 12, 14, 20, 23, 28, 30, 36**
Next, we calculate the quartiles:
### Part 1: Second Quartile (Q2)
The second quartile (Q2) is the median of the dataset. Since there are 10 numbers (even), we take the average of the 5th and 6th values in the sorted list.
- 5th value: 14
- 6th value: 20
\[
Q2 = \frac{14 + 20}{2} = \frac{34}{2} = 17
\]
### Part 2: First Quartile (Q1)
The first quartile (Q1) is the median of the first half of the data (the lower half). The first half includes the first 5 values:
**4, 9, 11, 12, 14**
Since there are 5 numbers, the median here is the 3rd value:
- 3rd value: 11
Thus,
\[
Q1 = 11
\]
### Part 3: Third Quartile (Q3)
The third quartile (Q3) is the median of the second half of the data (the upper half). The second half includes the last 5 values:
**20, 23, 28, 30, 36**
Again, since there are 5 numbers, the median is the 3rd value:
- 3rd value: 28
Thus,
\[
Q3 = 28
\]
### Final Answers
- Second Quartile (Q2): **17**
- First Quartile (Q1): **11**
- Third Quartile (Q3): **28**
Given set: **4, 9, 11, 20, 12, 23, 30, 36, 14, 28**
Sorted set: **4, 9, 11, 12, 14, 20, 23, 28, 30, 36**
Next, we calculate the quartiles:
### Part 1: Second Quartile (Q2)
The second quartile (Q2) is the median of the dataset. Since there are 10 numbers (even), we take the average of the 5th and 6th values in the sorted list.
- 5th value: 14
- 6th value: 20
\[
Q2 = \frac{14 + 20}{2} = \frac{34}{2} = 17
\]
### Part 2: First Quartile (Q1)
The first quartile (Q1) is the median of the first half of the data (the lower half). The first half includes the first 5 values:
**4, 9, 11, 12, 14**
Since there are 5 numbers, the median here is the 3rd value:
- 3rd value: 11
Thus,
\[
Q1 = 11
\]
### Part 3: Third Quartile (Q3)
The third quartile (Q3) is the median of the second half of the data (the upper half). The second half includes the last 5 values:
**20, 23, 28, 30, 36**
Again, since there are 5 numbers, the median is the 3rd value:
- 3rd value: 28
Thus,
\[
Q3 = 28
\]
### Final Answers
- Second Quartile (Q2): **17**
- First Quartile (Q1): **11**
- Third Quartile (Q3): **28**