Let's solve this step by step based on the provided results.
1. Interquartile Range (IQR) for Grade 7:
The interquartile range (IQR) is a measure of statistical dispersion, or how spread out the numbers in a data set are. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). For the Grade 7 data:
- First Quartile, Q1: 18.5
- Third Quartile, Q3: 23.25
- IQR: [tex]\(Q3 - Q1 = 23.25 - 18.5 = 4.75\)[/tex]
Therefore, the interquartile range for the Grade 7 data is 4.75.
2. Interquartile Range (IQR) for Grade 8:
For the Grade 8 data:
- First Quartile, Q1: 19.5
- Third Quartile, Q3: 24.75
- IQR: [tex]\(Q3 - Q1 = 24.75 - 19.5 = 5.25\)[/tex]
Therefore, the interquartile range for the Grade 8 data is 5.25.
3. Difference of the Medians of the Two Data Sets:
The median is the middle value of the data set. For Grade 7 and Grade 8:
- Median for Grade 7: 20.5
- Median for Grade 8: 22.5
The difference between the medians: [tex]\( |22.5 - 20.5| = 2.0 \)[/tex]
Therefore, the difference of the medians of the two data sets is 2.0.
4. Difference in Terms of IQR:
We compare the difference of the medians (2.0) to the larger IQR of the two data sets, which is 5.25 (Grade 8):
[tex]\[
\text{Difference in terms of IQR} = \frac{\text{Difference of medians}}{\text{Larger IQR}} = \frac{2.0}{5.25} \approx 0.381
\][/tex]
Therefore, the difference is about 0.381 times the interquartile range of either data set.
Putting it all together for the drop-down selections:
- The interquartile range for the grade 7 data is 4.75.
- The interquartile range for the grade 8 data is 5.25.
- The difference of the medians of the two data sets is 2.0.
- The difference is about 0.381 times the interquartile range of either data set.
