Question

A dendritic tree is a branched structure that emanates from the body of a nerve cell. As part of a study of brain development, 36 nerve cells were taken from the brains of newborn guinea pigs. The investigators counted the number of dendritic branch segments emanating from each nerve cell. The numbers were as follows: 14 \(\begin{array}{lllllllll}23 & 30 & 54 & 28 & 31 & 29 & 34 & 35 & 30 \\ 27 & 21 & 43 & 51 & 35 & 51 & 49 & 35 & 24 \\ 26 & 29 & 21 & 29 & 37 & 27 & 28 & 33 & 33 \\ 23 & 37 & 27 & 40 & 48 & 41 & 20 & 30 & 57\end{array}\) Construct a dotplot of the data.

Short answer

A dotplot has been constructed by sorting the data, drawing a number line, plotting the dendritic branch segment counts as dots, and properly titling and labeling the plot.

Step-by-step solution

Collect and Sort Data

First, collect all data points and write them in ascending order. Sorting the data will make it easier to create the dotplot.

Create a Number Line

Draw a horizontal line, which represents a number line with appropriate scale to accommodate the smallest and largest data points. Label this line with the range of values from the sorted data list.

Plot the Data Points

Above the number line, mark a dot above each corresponding value on the number line for every dendritic branch segment count. If a value occurs more than once, stack the dots vertically.

Title and Label the Dotplot

Provide a title for the dotplot and label the axes appropriately. The horizontal axis represents the number of dendritic branch segments, and the vertical axis represents the frequency of each count.

Key concepts

Statistical Data Representation

Statistical data representation is a crucial element in the analysis and interpretation of data. One simple yet powerful way to visually display data is through a dotplot, which allows us to see patterns and distributions at a glance.

A dotplot is a type of graph that represents frequency of data points through dots plotted along a single axis. It is ideal for small data sets where individual data values and their frequency can be easily appreciated. When creating a dotplot, a number line is drawn to represent the range of data. Individual data points are then plotted as dots above their corresponding values. If several data points share the same value, their dots are stacked vertically.

This method is particularly efficient in spotting outliers, gaps, clusters, and the overall spread of data. It's a fundamental tool for exploring data in descriptive statistics and can serve as a stepping stone to more complex graphical representations.

Descriptive Statistics

Descriptive statistics provide a way to summarize and describe the features of a data set. Key measures such as the mean, median, mode, variance, and standard deviation offer insights into the data’s central tendency and variability.

However, descriptive statistics encompass more than just numerical summaries; graphical tools like dotplots play a vital role. A dotplot presents a 'picture' of the data, making it accessible even to those with a limited statistical background. By visualizing data, we can identify trends and patterns not readily apparent from mere numbers.

In the case of the dendritic tree study, constructing a dotplot for the number of dendritic branch segments provides a visual summary of the neuronal structures in newborn guinea pigs. It offers an initial sense of the data before delving into numerical descriptive statistics, highlighting characteristics like skewness, peaks, or concentration of values.

Biostatistics

Biostatistics is the application of statistics to biological fields such as medicine, biology, and public health. It is essential for designing experiments, analyzing biological data, and understanding results in a biological context.

In biostatistics, dotplots can be particularly useful for the initial exploration of data. They allow researchers to quickly check the distribution of measurements, such as the dendritic branch segments, across a sample. They can spot potential biological variations or anomalies that could lead to further hypothesis testing or experiments.

For example, a dotplot of dendritic branch segments would visually reveal whether most neurons had a similar number of segments or if there were significant variations. Such graphical representation is vital for understanding the biological implications of the data and planning subsequent analysis, underlining the intersection of biostatistics with descriptive statistics and overall data representation.