Question

Find the quartiles for the given dataset. If needed, express your answer as a decimal rounded to the nearest tenth.

35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70

(2 points)
Q1
:
; Q2
or the median:
; Q3
:

Answer 1

To find the quartiles for the given dataset, we can follow these steps:

1. **Order the data**: The provided data is already in ascending order:
35, 40, 40, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70

2. **Calculate Q2 (the median)**:
- Since there are 13 data points (an odd number), Q2 will be the middle value:
\[
Q2 = \text{value at position } \left( \frac{n + 1}{2} \right) = \text{value at position } \left( \frac{13 + 1}{2} \right) = \text{value at position } 7
\]
- The 7th value in the ordered dataset is 50, so:
\[
Q2 = 50
\]

3. **Calculate Q1 (the first quartile)**:
- Q1 is the median of the first half of the data (the first 6 values):
35, 40, 40, 45, 45, 50
- There are 6 data points, so the median is the average of the 3rd and 4th values:
\[
Q1 = \frac{(40 + 45)}{2} = \frac{85}{2} = 42.5
\]

4. **Calculate Q3 (the third quartile)**:
- Q3 is the median of the second half of the data (the last 6 values):
50, 50, 55, 60, 60, 65, 70
- Similar to Q1, there are 6 data points here, so Q3 is the average of the 3rd and 4th values:
\[
Q3 = \frac{(60 + 60)}{2} = \frac{120}{2} = 60
\]

Putting it all together, we have:
- \( Q1 = 42.5 \)
- \( Q2 = 50 \)
- \( Q3 = 60 \)

Thus, the final answers are:
- \( Q1: 42.5 \)
- \( Q2: 50 \)
- \( Q3: 60 \)