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The table shows the growth, in centimeters, of plants in two different soils after two weeks.

Soil Type vs. Plant Growth

[tex]\[
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Soil A & 3.1 & 5.2 & 4.6 & 3.8 & 6.0 & 4.3 & 3.7 & 4.0 & 3.5 & 3.5 \\
\hline
Soil B & 2.9 & 3.8 & 5.0 & 4.8 & 4.5 & 3.9 & 3.9 & 4.4 & 5.5 & 4.1 \\
\hline
\end{tabular}
\][/tex]

Which statement explains which soil tended to have greater growth?

A. Soil A had greater growth because its data have a greater standard deviation.
B. Soil A had greater growth because its data have a greater mean.
C. Soil B had greater growth because its data have a greater interquartile range.
D. Soil B had greater growth because its data have a greater median.

Sagot :

GinnyAnswer
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.
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