Question

What are the quartiles for the
given dataset?
115, 117, 120, 122, 125, 125,
127, 128, 131, 132, 136, 136,
140
: 122; : 127.5;
: 132
Q1 Q2
Q3
: 121; : 127; :
134
Q1 Q2 Q3
: 115; : 127; :
140
Q1 Q2 Q3
: 121; : 127.5;
: 134
Q1 Q2
Q

Answer 1

To calculate the quartiles (Q1, Q2, Q3) for the given dataset, we first need to arrange the data in ascending order (though it seems to already be arranged). The dataset you provided is:

115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140

### Step 1: Identify Q2 (Median)

The median (Q2) is the middle value. Since there are 13 values in the dataset (an odd number), the median is located at position (13 + 1) / 2 = 7th position.

- **Q2 (Median)**: 127

### Step 2: Identify Q1

Q1 is the median of the first half of the data (the lower half), which consists of the first six numbers:

115, 117, 120, 122, 125, 125

The median of these 6 numbers (an even number) is the average of the 3rd and 4th values:

- **Q1**: (120 + 122) / 2 = 121

### Step 3: Identify Q3

Q3 is the median of the second half of the data (the upper half), which consists of the last six numbers:

128, 131, 132, 136, 136, 140

The median of these 6 numbers (an even number) is the average of the 3rd and 4th values:

- **Q3**: (132 + 136) / 2 = 134

### Summary of Quartiles
- **Q1**: 121
- **Q2**: 127
- **Q3**: 134

Thus, the correct values for the quartiles based on your options are:
- Q1: 121
- Q2: 127
- Q3: 134