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)

Answer 1

To find the quartiles of the given dataset, we first need to organize the data in ascending order, which it already is:

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

Next, we calculate the quartiles:

1. **Median (Q2):**
The median is the middle value of the dataset. Since there are 13 numbers (an odd count), the median is the value at the 7th position:

- Median (Q2) = 50

2. **Lower Quartile (Q1):**
Q1 is the median of the first half of the data (the first 6 numbers):

- First half: 35, 40, 40, 45, 45, 50
- There are 6 numbers, so the median is the average of the 3rd and 4th values:
- Q1 = (40 + 45) / 2 = 42.5

3. **Upper Quartile (Q3):**
Q3 is the median of the second half of the data (the last 6 numbers):

- Second half: 50, 50, 55, 60, 60, 65, 70
- Again, there are 6 numbers, so the median is the average of the 3rd and 4th values:
- Q3 = (60 + 60) / 2 = 60

Now we have the quartiles:

- Q1 = 42.5
- Q2 (Median) = 50
- Q3 = 60

So, the quartiles are:

- Q1: 42.5
- Q2: 50
- Q3: 60

**Therefore:**
- Q1: 42.5
- Q2 (Median): 50
- Q3: 60