Question

In a behavioral study of the fruitfly Drosophila melanogaster, a biologist measured, for individual flies, the total time spent preening during a 6 -minute observation period. The following are the preening times (sec) for 20 flies: \(^{54}\) $$ \begin{array}{lllll} 34 & 24 & 10 & 16 & 52 \\ 76 & 33 & 31 & 46 & 24 \\ 18 & 26 & 57 & 32 & 25 \\ 48 & 22 & 48 & 29 & 19 \end{array} $$ (a) Determine the mode (s). (b) Calculate the range. (c) Construct a dotplot of the data.

Short answer

The mode(s) of the data set is/are the value(s) that appear most frequently. The range is the difference between the maximum and minimum preening times. A dotplot is constructed by placing dots above a number line for each occurrence of the preening times.

Step-by-step solution

Find the Mode

To determine the mode of the data, we list the preening times in order and find the most frequently occurring value(s).

Calculate the Range

The range is the difference between the maximum and minimum values in the data set. To find the range, identify these two values from the ordered list and subtract the minimum value from the maximum value.

Construct a Dotplot

To construct a dotplot, draw a number line that spans the range of the data. Then, above each number corresponding to a preening time, place a dot for each time that value occurs in the data set.

Key concepts

Mode in Statistics

Understanding the concept of the mode in statistics is akin to finding the crowd favorite in a list of numbers—it's the value that appears most frequently. For instance, when a biologist measures how long various fruit flies spend preening, the mode represents the preening time observed most often among all the flies. If multiple values occur with the same highest frequency, each of these values is a mode, and we describe the data as bimodal or multimodal respectively. Identifying the mode is straightforward and doesn't require complex calculations; simply tally up how often each value appears, and the highest frequency points you to the mode.

Being a measure of central tendency, the mode provides a quick glimpse at typical behavior in the data. Unlike the mean or median, which are affected by extreme values, the mode can give a clearer picture of the most common state or behavior, particularly in qualitative data where numerical averages are not meaningful.

Range in Statistics

The range in statistics is a measure of how spread out data values are and is the simplest form of variability. By subtracting the smallest value from the largest, you capture the entire sweep of data in a single number. For a biologist timing fruit fly preening behavior, knowing the range helps understand the diversity in preening times—from the least preoccupied to the most meticulous groomer.

This measure has its limitations, primarily being sensitive to outliers. A single unusual observation can skew the range significantly. Despite this, the range remains a handy tool for getting a basic sense of variation among data points.

Dotplot Representation

A dotplot is like a snapshot of data, providing a visual representation that's as simple as it is effective. Imagine plotting the time each fruit fly spends preening on a horizontal line: each fly's preening time gets its own dot. This type of graph allows researchers to quickly discern patterns, such as clusters of flies with similar behavior, or spot outliers that stand out from the group. Dotplots are particularly useful for small data sets, making trends and modes readily apparent without any complex analysis.

While dotplots offer a clear visual summary, they are less informative for larger, more complex data sets, which might require more sophisticated graphical representations to reveal the underlying patterns and relationships.

Behavioral Study of Drosophila melanogaster

Drosophila melanogaster, or the common fruit fly, is a staple in genetic research and behavioral studies given its simple genetic makeup and fast reproduction cycle. When biologists measure aspects like preening time, they seek insights into the normal behaviors or effects of genetic modifications. Behavioral studies often involve collecting data on various actions or reactions, which can then be analyzed statistically to identify patterns and draw conclusions.

The data collected from observing Drosophila can be complex, necessitating a thorough understanding of both statistical concepts and biological context to interpret the findings accurately.

Data Analysis in Biology

Data analysis in biology is a cornerstone of understanding complex living systems. Whether examining fruit fly behavior or mapping out ecosystems, biologists rely on statistical tools to make sense of their observations. From simple statistics like mode and range to more elaborate inferential techniques, each method offers a lens to view and interpret the raw data.

In studies like the Drosophila preening observation, statistical analysis helps determine whether observed behaviors are random or part of a larger pattern, potentially linked to underlying genetic traits or environmental factors. It's crucial for biologists to select appropriate data visualization methods, such as dotplots, to communicate their findings effectively to both the scientific community and the public.