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4) the box plots show the heights of sunflower plants in a random sample of 40 plants from field a and a random sample of 40 plants

Question

4) The box plots show the heights of sunflower plants in a random sample of 40 plants from Field A and a random sample of 40 plants from Field B. 4) Which field typically has shorter plants?Explain. (1) Field B typically has shorter plants. You can tell because the median of its samples is less than that of the other field. (1) Which sunflower field has plants with more consistent heights?Explain. (1) median typically has plants with more IQR eights. You can tell because the ? square 4 that of the other field. Heights of Sunflower Plants Field A square Field B 2 4 6 8 10 12 Height (ft)

Answer

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Whitney Professional · Tutor for 6 years

Answer

To answer the questions, we will analyze the information provided in the picture details step by step.Step 1: Determine which field typically has shorter plants.To do this, we compare the median heights of the sunflower plants in both fields. The median is a measure of central tendency that indicates the middle value of a data set when it is ordered from least to greatest.- Field A has a median height of 5 feet.- Field B has a median height of 4 feet.Since the median height of Field B is less than that of Field A, we can conclude that Field B typically has shorter plants.Answer: (1) Field B typically has shorter plants because the median of its samples is less than that of Field A.Step 2: Determine which sunflower field has plants with more consistent heights.To assess consistency in heights, we look at the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). The IQR represents the middle 50% of the data and is a measure of variability; a smaller IQR indicates less variability and more consistency in the data.- Field A has a first quartile at 4 feet and a third quartile at 6 feet, so the IQR is 6 - 4 = 2 feet.- Field B has a first quartile at 3 feet and a third quartile at 5 feet, so the IQR is 5 - 3 = 2 feet.Both fields have the same IQR of 2 feet, which means they have the same level of consistency in the heights of their sunflower plants based on the IQR.However, if we consider the overall range (maximum height - minimum height) as an additional measure of consistency:- Field A has a range of 10 - 3 = 7 feet.- Field B has a range of 11 - 2 = 9 feet.Field B has a greater overall range, which suggests more variability in the heights of its plants.Answer: Based on the IQR alone, both fields have the same level of consistency in plant heights. However, considering the overall range, Field A has plants with more consistent heights because the range of its samples is less than that of Field B.