Question

the table shows the growth, in centimeters, of plants in two different soils after two weeks soil type vs. plant growth 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 which statement explains which soil tended to have a greater growth? soil a had greater growth because its data have a greater standard deviation. soil a had greater growth because its data have a greater mean. soil b had greater growth because its data have a greater interquartile range soil b had greater growth because its data have a greater median.

Explanation:

Step1: Calculate median of Soil A

First, order Soil A data: 3.1, 3.5, 3.5, 3.7, 3.8, 4.0, 4.3, 4.6, 5.2, 6.0. There are 10 data - points. The median is the average of the 5th and 6th ordered values. Median of Soil A=$\frac{3.8 + 4.0}{2}=3.9$.

Step2: Calculate median of Soil B

Order Soil B data: 2.9, 3.8, 3.9, 3.9, 4.1, 4.4, 4.5, 4.8, 5.0, 5.5. There are 10 data - points. The median is the average of the 5th and 6th ordered values. Median of Soil B=$\frac{4.1+4.4}{2}=4.25$.

Step3: Compare medians

Since 4.25>3.9, Soil B has a greater median, which indicates that Soil B tended to have greater plant growth. Standard deviation and inter - quartile range measure the spread of data, not the central tendency related to overall growth. And we have not calculated the mean here, but the median comparison already gives the answer.

Answer:

Soil B had greater growth because its data have a greater median.