To find the quartiles \(Q1\), \(Q2\), and \(Q3\) for the dataset:
Dataset: 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Step 1: Order the data (already ordered in this case).
Step 2: Find the median (Q2).
- The dataset has 13 numbers, so the median is the middle number.
- The middle position is at \( \frac{13 + 1}{2} = 7^{th} \) number.
- The 7th number in the ordered list is 127.
So, \( Q2 = 127 \).
Step 3: Find \(Q1\) (the median of the first half of the data).
- The first half (lower half) of the data is: 115, 117, 120, 122, 125, 125.
- This subset has 6 numbers, so the median is the average of the 3rd and 4th numbers.
- The 3rd number is 120, and the 4th number is 122.
\[ Q1 = \frac{120 + 122}{2} = \frac{242}{2} = 121 \]
Step 4: Find \(Q3\) (the median of the second half of the data).
- The second half (upper half) of the data is: 128, 131, 132, 136, 136, 140.
- This subset also has 6 numbers, so the median is the average of the 3rd and 4th numbers.
- The 3rd number is 132, and the 4th number is 136.
\[ Q3 = \frac{132 + 136}{2} = \frac{268}{2} = 134 \]
Final Results:
- \( Q1 = 121 \)
- \( Q2 = 127 \)
- \( Q3 = 134 \)
The correct response is: Q1: 121; Q2: 127; Q3: 134