Let's analyze the given data to determine which soil tended to have greater growth. We will base our analysis on several statistical measurements: mean, median, standard deviation, and interquartile range (IQR).
### Soil Type vs. Plant Growth Data:
- Soil A: 3.1, 5.2, 4.6, 3.8, 6.0, 4.3, 3.7, 4.0, 3.5, 3.5
- Soil B: 2.9, 3.8, 5.0, 4.8, 4.5, 3.9, 3.9, 4.4, 5.5, 4.1
### Statistical Measures:
1. Mean (Average):
- [tex]\( \text{Mean of Soil A} = 4.17 \)[/tex]
- [tex]\( \text{Mean of Soil B} = 4.28 \)[/tex]
The mean shows the average growth of plants in each soil type. Soil B has a slightly higher mean compared to Soil A, indicating that on average, plants in Soil B grew more.
2. Median:
- [tex]\( \text{Median of Soil A} = 3.9 \)[/tex]
- [tex]\( \text{Median of Soil B} = 4.25 \)[/tex]
The median represents the middle value of the data set when it is ordered. Soil B has a higher median, showing that the central tendency of plant growth in Soil B is greater than in Soil A.
3. Standard Deviation:
- [tex]\( \text{Standard Deviation of Soil A} = 0.8391 \)[/tex]
- [tex]\( \text{Standard Deviation of Soil B} = 0.6925 \)[/tex]
The standard deviation measures the dispersion or variability in the data. Soil A has a higher standard deviation, indicating more variability in plant growth compared to Soil B.
4. Interquartile Range (IQR):
- [tex]\( \text{IQR of Soil A} = 0.975 \)[/tex]
- [tex]\( \text{IQR of Soil B} = 0.825 \)[/tex]
The IQR measures the range within which the middle 50% of the data values lie. Soil A has a higher IQR, indicating that the middle 50% of its growth data is more spread out than that of Soil B.
### Conclusion:
- Soil A has a greater standard deviation, which means it has more variability in the growth data.
- Soil A also has a greater IQR, indicating a wider middle range of growth measurements.
- However, Soil B has both a higher mean and a higher median, indicating a higher central tendency in the growth data compared to Soil A.
Therefore, the statement that best explains which soil tended to have greater growth is:
- Soil B had greater growth because its data have a greater median.
The higher mean and median values in Soil B's data suggest that plants generally grew more in this soil type.
