To find the quartiles for this dataset, we first need to order the data from smallest to largest:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Since this dataset has 13 values, the median is the value at position (13+1)/2 = 7th position, which is 127.
Next, we need to find the lower quartile (Q1) and upper quartile (Q3). To do this, we need to find the median of the first half and second half of the dataset respectively:
Lower half: 115, 117, 120, 122, 125, 125, 127
Upper half: 128, 131, 132, 136, 136, 140
For the lower half, the median is the value at position (7+1)/2 = 4th position, which is 122. For the upper half, the median is the value at position (6+1)/2 = 3rd position, which is 132.
Therefore, the quartiles for this dataset are:
Q1 = 122
Q2 (Median) = 127
Q3 = 132
What are the quartiles for the given dataset?
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
3 answers
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I apologize for the mistake in my previous response. Let me correct the quartiles for the given dataset:
1. The dataset in ascending order is: 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
2. The median (Q2) is the middle value of the dataset, which is the value at position (13+1)/2 = 7th position, so Q2 = 127.
3. To find Q1 and Q3, you need to find the medians of the lower half of the dataset and the upper half of the dataset.
- Lower half: 115, 117, 120, 122, 125, 125
The median of the lower half is the value at position (6+1)/2 = 3.5th position, which is the average of the 3rd and 4th values: (120+122)/2 = 121.
- Upper half: 128, 131, 132, 136, 136, 140
The median of the upper half is the value at position (6+1)/2 = 3.5th position, which is the average of the 4th and 5th values: (132+136)/2 = 134.
Therefore, the correct quartiles for this dataset are:
Q1 = 121
Q2 (Median) = 127
Q3 = 134
1. The dataset in ascending order is: 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
2. The median (Q2) is the middle value of the dataset, which is the value at position (13+1)/2 = 7th position, so Q2 = 127.
3. To find Q1 and Q3, you need to find the medians of the lower half of the dataset and the upper half of the dataset.
- Lower half: 115, 117, 120, 122, 125, 125
The median of the lower half is the value at position (6+1)/2 = 3.5th position, which is the average of the 3rd and 4th values: (120+122)/2 = 121.
- Upper half: 128, 131, 132, 136, 136, 140
The median of the upper half is the value at position (6+1)/2 = 3.5th position, which is the average of the 4th and 5th values: (132+136)/2 = 134.
Therefore, the correct quartiles for this dataset are:
Q1 = 121
Q2 (Median) = 127
Q3 = 134