Question

To calibrate a standard curve for assaying protein concentrations, a plant pathologist used a spectrophotometer to measure the absorbance of light (wavelength $500\mathrm{nm}$ ) by a protein solution. The results of 27 replicate assays of a standard solution containing $60\mu \mathrm{g}$ protein per $\mathrm{ml}$ water were as follows: ${}^{55}$ $$\begin{array}{lllll}0.111& 0.115& 0.115& 0.110& 0.099\\ 0.121& 0.107& 0.107& 0.100& 0.110\\ 0.106& 0.116& 0.098& 0.116& 0.108\\ 0.098& 0.120& 0.123& 0.124& 0.122\\ 0.116& 0.130& 0.114& 0.100& 0.123\\ 0.119& 0.107& & & \end{array}$$ Construct a frequency distribution and display it as a table and as a histogram.

Short answer

Organize the data, determine the range, create equal intervals for bins, tally the frequencies for each bin, construct a frequency distribution table, and then create a histogram based on the frequency distribution.

Step-by-step solution

Organize the Data

Collect all the absorbance values and list them in ascending order. This will help in determining the range of values and the intervals for constructing the frequency distribution.

Determine the Range

Find the range of the data by subtracting the smallest absorbance value from the largest one.

Create Intervals

Divide the range into a set of equal intervals to use as bins for the frequency distribution. The number of intervals can be chosen based on the square root of the number of data points or using Sturges' formula.

Tally the Frequencies

Count the number of absorbance values that fall into each interval and record this count as the frequency for that interval.

Construct the Frequency Distribution Table

Create a table with two columns: one for the intervals (bins) and one for the corresponding frequencies.

Create the Histogram

Draw a histogram using the intervals on the x-axis and the frequencies on the y-axis, making sure each bar's height corresponds to the frequency of the interval.

Key concepts

Spectrophotometry

Spectrophotometry is a powerful analytical technique used to measure the absorbance or transmission of light by a material. When applied to the study of proteins, it allows researchers to determine protein concentrations by exploiting the fact that proteins can absorb specific wavelengths of light.

In the given exercise, a plant pathologist employs spectrophotometry to measure the absorbance at a wavelength of 500 nm. This particular wavelength is chosen because the protein of interest absorbs light maximally at this wavelength. The data obtained reveal how much light the protein solution is absorbing, which correlates with its concentration.

To assure accurate readings, the spectrophotometer must be calibrated, which is often done using a standard curve - a plot of known concentrations against their corresponding absorbance values. The scientist can then interpolate the concentration of an unknown sample based on its absorbance. For reliable results, multiple replicate assays should be performed, as in the exercise with 27 measurements, to account for experimental variation and enhance precision.

Frequency Distribution

Frequency distribution is a method used to organize data and present it in a summarized form. It's particularly helpful in identifying patterns and understanding the spread of data points in a given dataset.

In the context of our exercise, frequency distribution is utilized to show how often each absorbance value occurs within the range of collected data. After organizing the absorbance readings in ascending order, the data range is obtained by subtracting the smallest value from the largest one.

Next, equal intervals or bins are determined to categorize the dataset. Choices regarding the number of bins can be made based on the square root of the number of data points or using Sturges' formula. Each absorbance reading is then tallied into the appropriate interval, creating a frequency for each bin, which is essential to visualizing the data's distribution in a tabular form or as a histogram. This process helps in understanding the concentration uniformity of the replicated assays.

Histogram Construction

Histograms are a type of bar graph that visually represents the frequency distribution of numeric data. Constructing histograms is an excellent way to visualize the patterns and distribution within a dataset and is commonly used in various scientific research fields, including protein assay analysis.

When constructing a histogram for the given exercise, the x-axis represents the intervals or bins of absorbance values, while the y-axis represents their corresponding frequencies. Each bar's height correlates directly with the frequency count of the interval, providing a visual snapshot of data concentration within specific ranges. In our protein assay, the histogram would show the spread and consistency of the absorbance measurements, highlighting any potential anomalies or patterns in the data.

This graphical representation provides a quick way to assess whether the replicated assays are consistent with each other or if there are outliers that could indicate errors in the measurement or sample preparation process. Histograms are a fundamental tool in conveying complex data in a digestible format that can be easily interpreted by those analyzing the results of experiments such as protein concentration assays.