Question
Answer the question below and round to the nearest tenth.
find the interquartile range for the following dataset: 3, 5, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 25
find the interquartile range for the following dataset: 3, 5, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 25
Answers
Answered by
GPT-4o mini
To find the interquartile range (IQR) of the given dataset, we will first order the data (which is already ordered here) and then calculate the first quartile (Q1) and the third quartile (Q3).
The dataset is:
3, 5, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 25
1. **Determine the quartiles:**
- The total number of data points (n) is 13.
- To find Q1 (the first quartile), we can find the median of the first half of the data (the first 6 numbers since n is odd).
- The first half: 3, 5, 7, 8, 9, 10
The median of the first half (Q1) is:
\[
Q1 = \frac{7 + 8}{2} = 7.5
\]
- To find Q3 (the third quartile), we take the median of the second half of the data (the last 6 numbers).
- The second half: 12, 13, 15, 18, 20, 22, 25
The median of the second half (Q3) is:
\[
Q3 = \frac{18 + 20}{2} = 19
\]
2. **Calculate the interquartile range (IQR):**
\[
\text{IQR} = Q3 - Q1 = 19 - 7.5 = 11.5
\]
Thus, the interquartile range for the dataset is **11.5**.
The dataset is:
3, 5, 7, 8, 9, 10, 12, 13, 15, 18, 20, 22, 25
1. **Determine the quartiles:**
- The total number of data points (n) is 13.
- To find Q1 (the first quartile), we can find the median of the first half of the data (the first 6 numbers since n is odd).
- The first half: 3, 5, 7, 8, 9, 10
The median of the first half (Q1) is:
\[
Q1 = \frac{7 + 8}{2} = 7.5
\]
- To find Q3 (the third quartile), we take the median of the second half of the data (the last 6 numbers).
- The second half: 12, 13, 15, 18, 20, 22, 25
The median of the second half (Q3) is:
\[
Q3 = \frac{18 + 20}{2} = 19
\]
2. **Calculate the interquartile range (IQR):**
\[
\text{IQR} = Q3 - Q1 = 19 - 7.5 = 11.5
\]
Thus, the interquartile range for the dataset is **11.5**.