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Statistics Unit Test
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Question
The highest temperatures measured at Death Valley, California, from 1995 to 2004 are given as a dataset.
127, 125, 125, 129, 123, 126, 127, 128, 128, 125
Find the range and the interquartile range of the dataset.
(1 point)
The range is
, and interquartile range is
.
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Answers
GPT-4o mini
To calculate the range and the interquartile range (IQR) of the dataset provided, we will follow these steps:
### Dataset
The dataset is:
127, 125, 125, 129, 123, 126, 127, 128, 128, 125
### Step 1: Calculate the Range
The range is calculated as the difference between the maximum and minimum values in the dataset.
- **Maximum value**: 129
- **Minimum value**: 123
\[ \text{Range} = \text{Max} - \text{Min} = 129 - 123 = 6 \]
### Step 2: Calculate the Interquartile Range (IQR)
The interquartile range is the difference between the first quartile (Q1) and the third quartile (Q3).
#### Step 2a: Sort the data
First, we sort the data in ascending order:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
#### Step 2b: Find the first quartile (Q1)
- Q1 is the median of the first half of the data (the lower half).
- Lower half = 123, 125, 125, 125, 126
- Median of lower half (Q1) is the middle value, which is 125.
#### Step 2c: Find the third quartile (Q3)
- Q3 is the median of the second half of the data (the upper half).
- Upper half = 127, 127, 128, 128, 129
- Median of upper half (Q3) is the middle value, which is 128.
#### Step 2d: Calculate the IQR
\[ \text{IQR} = Q3 - Q1 = 128 - 125 = 3 \]
### Final Results
- The range is **6**
- The interquartile range is **3**
So the answers are:
- The range is **6**, and the interquartile range is **3**.
### Dataset
The dataset is:
127, 125, 125, 129, 123, 126, 127, 128, 128, 125
### Step 1: Calculate the Range
The range is calculated as the difference between the maximum and minimum values in the dataset.
- **Maximum value**: 129
- **Minimum value**: 123
\[ \text{Range} = \text{Max} - \text{Min} = 129 - 123 = 6 \]
### Step 2: Calculate the Interquartile Range (IQR)
The interquartile range is the difference between the first quartile (Q1) and the third quartile (Q3).
#### Step 2a: Sort the data
First, we sort the data in ascending order:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
#### Step 2b: Find the first quartile (Q1)
- Q1 is the median of the first half of the data (the lower half).
- Lower half = 123, 125, 125, 125, 126
- Median of lower half (Q1) is the middle value, which is 125.
#### Step 2c: Find the third quartile (Q3)
- Q3 is the median of the second half of the data (the upper half).
- Upper half = 127, 127, 128, 128, 129
- Median of upper half (Q3) is the middle value, which is 128.
#### Step 2d: Calculate the IQR
\[ \text{IQR} = Q3 - Q1 = 128 - 125 = 3 \]
### Final Results
- The range is **6**
- The interquartile range is **3**
So the answers are:
- The range is **6**, and the interquartile range is **3**.