Problem 2 - AP Biology Premium Prep 2021

Question

The height of six trees is measured. Is plant 6 taller than the median for all six trees? $$\begin{array}{|c|c|} \hline \text { Plant } & \begin{array}{c} \text { Height } \\ \text { (inches) } \end{array} \\ \hline 1 & 67 \\ \hline 2 & 61 \\ \hline \hline 3 & 72 \\ \hline 4 & 71 \\ \hline 5 & 66 \\ \hline 6 & 68 \\ \hline \end{array}$$ (A) Yes, the median is 67.3 . (B) No, the median is 67.3 . (C) Yes, the median is 67.5 . (D) No, the median is 67.5 .

Step-by-Step Solution

Answer

Yes, the median is 67.5.

Step 1: List the heights in order

First, let's arrange the given heights of the trees in ascending order: 61, 66, 67, 68, 71, 72

Step 2: Find the median height

The median height of the trees is the middle value(s) of the ordered list. Since there are six trees, we have an even number of heights, so the median will be the average of the two middle values. The two middle values are 67 and 68. Let's calculate the median height: Median height = \(\frac{67+68}{2}\)

Step 3: Calculate the median height

Now, calculate the median height: Median height = \(\frac{67+68}{2} = \frac{135}{2} = 67.5\)

Step 4: Compare Plant 6's height to the median height

Plant 6's height is 68 inches. The median height of all six trees is 67.5 inches. Since 68 > 67.5, plant 6 is taller than the median height.

Step 5: Choose the correct answer option

Based on our analysis, plant 6 is taller than the median height (67.5 inches). Therefore, the correct answer is: (C) Yes, the median is 67.5 .

Key Concepts

Statistics in Biology

Understanding statistics in the field of biology is crucial for interpreting and analyzing quantitative data. In the context of the exercise provided, the concept of the median plays a significant role. The median is a measure of central tendency that represents the middle value in a sorted list of numbers. In biological data, which can involve measurements like the height of trees, weight of organisms, or number of leaves, finding the median gives us a sense of the 'center' of the data set.

In our example, the median height helps determine whether Plant 6 is of above-average height compared to its peers. This kind of analysis is fundamental when biologists need to understand traits within a population or compare various sub-groups within a habitat. When faced with skewed data or outliers, the median can sometimes provide a better representation of a typical value than the mean, as it is less influenced by extreme values. Given that biological data can often exhibit these characteristics, the median is a valuable statistic to comprehend and calculate accurately.

Data Analysis in Biology

Data analysis in biology often involves various statistical concepts to manage and interpret biological data effectively. The exercise we are considering involves a simple yet powerful analytical technique—ordering data points and calculating the median. When biologists collect data, such as heights of plants, sequencing genetic material, or observing behavioral patterns, they are confronted with raw data that must be organized meaningfully.

By ordering the heights of the trees from shortest to tallest, the concept of sorting data becomes evident; it is the first step before a more comprehensive analysis can occur. Upon sorting the data, calculating the median is a method to summarize the data set. This is a clear example of how raw biological data can be transformed into an insightful statistical measure. The importance of such analysis is multifaceted, for it can influence conservation attempts, inform breeding programs, or shape ecological forecasting.

AP Biology Statistical Concepts

In AP Biology, understanding statistical concepts is fundamental for students, as these tools are used to analyze experiments and understand biological phenomena. The median height problem exemplifies the application of descriptive statistics, which are used to describe basic features of the data in a study. In solving the exercise, students learn to determine the median in a hands-on approach, thereby gaining practical experience with the concept.

As part of the AP Biology curriculum, students must be familiar with not only the median but also other measures of central tendency such as the mean and mode, and measures of variability like range and standard deviation. These statistical concepts empower students to handle different types of biological data, draw conclusions, and lend support to biological assertions with quantitative evidence. Mastery of these principles is not only pivotal for high-scoring exam responses but also in cultivating a rigorous scientific mindset.