To determine the low, [tex]\( Q_1 \)[/tex], median, [tex]\( Q_3 \)[/tex], and high, let's follow the steps systematically.
1. Observe the given data:
- Low: 7
- Median: 10
- High: 17
2. The median is given as 10, which divides the dataset into two halves.
3. To find [tex]\( Q_1 \)[/tex] (the first quartile), which represents the 25th percentile, we consider it to be the midpoint between the low value (7) and the median (10). Thus, we calculate [tex]\( Q_1 \)[/tex] as:
[tex]\[
Q_1 = \frac{\text{Low} + \text{Median}}{2} = \frac{7 + 10}{2} = \frac{17}{2} = 8.5
\][/tex]
4. To find [tex]\( Q_3 \)[/tex] (the third quartile), which represents the 75th percentile, we consider it to be the midpoint between the median (10) and the high value (17). Thus, we calculate [tex]\( Q_3 \)[/tex] as:
[tex]\[
Q_3 = \frac{\text{Median} + \text{High}}{2} = \frac{10 + 17}{2} = \frac{27}{2} = 13.5
\][/tex]
5. Summarizing all values, we have:
- Low: 7
- [tex]\( Q_1 \)[/tex]: 8.5
- Median: 10
- [tex]\( Q_3 \)[/tex]: 13.5
- High: 17
In conclusion, the values are as follows:
- Low: 7
- [tex]\( Q_1 \)[/tex]: 8.5
- Median: 10
- [tex]\( Q_3 \)[/tex]: 13.5
- High: 17
