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 the mean of Soil A

$\bar{x}_A=\frac{3.1 + 5.2+4.6+3.8+6.0+4.3+3.7+4.0+3.5+3.5}{10}=\frac{42.7}{10} = 4.27$

Step2: Calculate the mean of Soil B

$\bar{x}_B=\frac{2.9+3.8+5.0+4.8+4.5+3.9+3.9+4.4+5.5+4.1}{10}=\frac{42.8}{10}=4.28$

Step3: Analyze the statements

• Standard - deviation measures the spread of data, not the central tendency related to growth.
• Inter - quartile range also measures the spread of data, not the growth amount.
• Since the mean of Soil B ($4.28$) is slightly greater than the mean of Soil A ($4.27$), Soil B has a greater average growth.

Answer:

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