Question

Six men with high serum cholesterol participated in a study to evaluate the effects of diet on cholesterol level. At the beginning of the study their serum cholesterol levels $(\mathrm{mg}/\mathrm{dl})$ were as follows: ${}^{22}$ $$\begin{array}{llllll}366& 327& 274& 292& 274& 230\end{array}$$ Determine the mean and the median.

Short answer

The mean serum cholesterol level is 293.83 mg/dl, and the median is 283 mg/dl.

Step-by-step solution

List the cholesterol levels

First, write down the serum cholesterol levels of the six men to make it easier to handle the numbers: 366, 327, 274, 292, 274, 230.

Calculate the mean

To find the mean cholesterol level, add up all the serum cholesterol levels and divide by the number of observations (individuals). Mean = $\frac{366+327+274+292+274+230}{6}$.

Compute the mean

Performing the calculation from Step 2 gives: Mean = $\frac{1763}{6}=293.83$ (rounded to two decimal places).

Order the cholesterol levels

For finding the median, arrange the cholesterol levels in ascending order: 230, 274, 274, 292, 327, 366.

Determine the median

Since there are an even number of observations, the median will be the average of the middle two numbers (the third and fourth values): Median = $\frac{274+292}{2}$.

Compute the median

Calculate the median value from the two middle numbers: Median = $\frac{566}{2}=283$.

Key concepts

Mean Calculation

Understanding how to calculate the mean value of a dataset is fundamental in various fields, including life sciences when analyzing cholesterol levels. The mean, commonly referred to as the average, is calculated by adding up all of the numbers in a dataset and then dividing by the count of the numbers. In the context of a serum cholesterol level study, this allows us to determine the average cholesterol level among participants.

For example, if we have cholesterol levels of 366, 327, 274, 292, 274, and 230 mg/dl, the mean would be computed as follows: Mean = \(\frac{366 + 327 + 274 + 292 + 274 + 230}{6}\).

By doing this calculation, we can observe the general trend in cholesterol levels among the study's subjects which is important for determining the overall success of dietary interventions.

Median Calculation

The median is another crucial statistical measure, especially when dealing with skewed datasets where outliers may distort the mean. It represents the middle value of an ordered dataset; when the dataset has an even number of values, as in our cholesterol study, the median is the average of the two middle numbers.

To find the median:

1. First, order the cholesterol levels from lowest to highest: 230, 274, 274, 292, 327, and 366.
2. Since there are six (an even number) of measurements, take the average of the third and fourth values (274 and 292).

Thus, the median calculation is: Median = \(\frac{274 + 292}{2} = 283\).

The median provides a measure that is not as sensitive to extreme values, making it very useful in representing a 'typical' value within the dataset.

Cholesterol Level Data Analysis

When studying serum cholesterol levels, data analysis is employed to make sense of the collected figures. Through statistical methods such as mean and median calculations, researchers can interpret the data to understand health trends. In our example, the mean gives us an idea of the overall cholesterol levels of the group, while the median offers insight into the central tendency of the dataset.

Data analysis in this context can also involve looking at the distribution of cholesterol levels, identifying outliers, and comparing pre-intervention data to post-intervention results to assess the effect of dietary changes. The use of charts and graphs can further aid in visualizing the data and extracting meaningful patterns and conclusions from the study. It's crucial for researchers to analyze such data accurately to make informed decisions about public health interventions.

Statistical Measures in Life Sciences

Statistical measures play a vital role in life sciences as they provide a way to make sense of data from experiments and studies. In addition to mean and median, researchers use a variety of statistical tools, including mode, range, variance, and standard deviation.

The application of these tools allows for the summarization of large datasets, estimation of population parameters, hypothesis testing, and the exploration of relationships between variables. In the context of a cholesterol study, utilizing these statistical measures can help decipher the normal levels, variance in response to treatments, and predict health outcomes. It's essential for students and researchers alike to have a solid grasp of these concepts to effectively conduct and interpret scientific research.