Question

What are the quartiles for the given data sets 115 117 120 122 125 127 128 131 132 136 136 140 A q1 115 q2 127 q3 140 B q1 121 q2 127 q3 134 C q1 121 Q2 127.5 Q3 134 D q1 122 Q2 127.5 Q3 132

Answer 1

To calculate the quartiles (Q1, Q2, Q3) for the given dataset, we must first arrange the data in ascending order (which it already is) and then use the following formulas:

- **Q1** (the first quartile) is the median of the lower half of the data.
- **Q2** (the second quartile) is the median of the data set.
- **Q3** (the third quartile) is the median of the upper half of the data.

**Given data:**
115, 117, 120, 122, 125, 127, 128, 131, 132, 136, 136, 140

1. **Count of Data Points**: There are 12 data points.
2. **Median (Q2)**:
Since there’s an even number of data points, the median will be the average of the 6th and 7th numbers:

Q2 = (127 + 128) / 2 = 127.5

3. **Q1**:
The lower half of the data (the first 6 numbers):
115, 117, 120, 122, 125, 127

The median of this lower half (Q1) is the average of the 3rd and 4th numbers:

Q1 = (120 + 122) / 2 = 121

4. **Q3**:
The upper half of the data (the last 6 numbers):
128, 131, 132, 136, 136, 140

The median of this upper half (Q3) is the average of the 3rd and 4th numbers:

Q3 = (132 + 136) / 2 = 134

**Quartiles for the given dataset**:
- Q1 = 121
- Q2 (Median) = 127.5
- Q3 = 134

**Between the options you provided:**
- **Option C** has Q1 = 121, Q2 = 127.5, Q3 = 134, which matches our calculated quartiles.

So, the quartiles for the given dataset are:
**Option C: Q1 = 121, Q2 = 127.5, Q3 = 134.**