Problem 3 - Clinical Chemistry

Question

The following chloride \((\mathrm{mmol} / \mathrm{L})\) results were obtained using a new analyzer: $$\begin{array}{rrrrrr} 106 & 111 & 104 & 106 & 112 & 110 \\ 115 & 127 & 83 & 110 & 108 & 109 \\ 83 & 119 & 105 & 106 & 108 & 114 \\ 120 & 100 & 107 & 110 & 109 & 102\end{array}$$ What is the median? a. \(108.5\) b. 105 c. 112 d. 107

Step-by-Step Solution

Answer

The median is 108.5

Step 1: Combine all values

Combine all the chloride values into a single list: 106, 111, 104, 106, 112, 110, 115, 127, 83, 110, 108, 109, 83, 119, 105, 106, 108, 114, 120, 100, 107, 110, 109, 102.

Step 2: Sort the values

Sort the combined list of chloride values in ascending order: 83, 83, 100, 102, 104, 105, 106, 106, 106, 107, 108, 108, 109, 109, 110, 110, 110, 111, 112, 114, 115, 119, 120, 127.

Step 3: Find the median position

Determine the median position in the list. Since there are 24 values (an even number), the median is the average of the 12th and 13th values in the sorted list.

Step 4: Identify the 12th and 13th values

Locate the 12th and 13th values in the sorted list: 108 and 109.

Step 5: Calculate the median

Calculate the median by finding the average of the 12th and 13th values: \( \frac{108 + 109}{2} = 108.5 \).

Key Concepts

Statistics in healthcare

Statistics play an essential role in healthcare as they help professionals make informed decisions. Knowing how to handle data is crucial for analyzing patient outcomes, treatment effectiveness, and diagnosing diseases. One common statistical measure is the median, which provides the middle value in a dataset. This measure is especially useful in clinical settings where extreme values can skew the results. For example, in analyzing patient chloride levels, knowing the median gives a central tendency that is less affected by unusually high or low values. These statistics contribute to better patient care and accurate diagnoses.

Analyzing clinical chemistry results

Clinical chemistry involves analyzing bodily fluids to diagnose and monitor diseases. Understanding the data from these analyses is crucial for patient care. When you receive a series of test results, one way to analyze them is by calculating the median. The median offers a clear picture of the central tendency without being skewed by outliers. In the exercise provided, chloride levels were collected using a new analyzer. To find the median, we combined and sorted all values. By identifying the middle values, we could determine the median chloride concentration. This is a practical method in clinical settings to summarize patient data effectively.

Median in data analysis

The median is a measure of central tendency that represents the middle value in a dataset. Calculating the median is straightforward:

• Combine all your data points.
• Sort them in ascending order.
• For an odd number of data points, the median is the middle number.
• For an even number of data points, it is the average of the two middle numbers.

In our example, we have 24 chloride values. After sorting them, we found the median by averaging the 12th and 13th values. This resulted in the median chloride level of 108.5 mmol/L. This statistical measure helps healthcare providers understand the typical range of patient results, making it vital for both research and clinical practice.