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The risk of developing iron deficiency is especially high during pregnancy. Detecting such a deficiency is complicated by the fact that some methods for determining iron status can be affected by the state of pregnancy itself. Consider the following data on transferrin receptor concentration for a sample of women with laboratory evidence of overt iron-deficiency anemia ("Serum Transferrin Receptor for the Detection of Iron Deficiency in Pregnancy," American journal of Clinical Nutrition [1991]: \(1077-1081\) ): $$ \begin{array}{llrlrl} 15.2 & 9.3 & 7.6 & 11.9 & 10.4 & 9.7 \\ 20.4 & 9.4 & 11.5 & 16.2 & 9.4 & 8.3 \end{array} $$ Compute the values of the sample mean and median. Why are these values different here? Which one do you regard as more representative of the sample, and why?

Short Answer

Expert verified
The sample mean and median were computed to be approximately 12.12 and 10.05 respectively. These values are different, suggesting a skew in the data, likely due to outliers. The median could be seen as more representative in this scenario because it is less sensitive to extreme values and thus offers a better 'typical' value than the mean.

Step by step solution

01

Compute the Sample Mean

First, let's tackle the calculation of the sample mean. To get the sample mean, you need to sum up all observed data points and divide by the number of observations. Here are the calculations:\n\n \[ \text{{mean}} = \frac{{15.2+9.3+7.6+11.9+10.4+9.7+20.4+9.4+11.5+16.2+9.4+8.3}}{12} \]
02

Compute the Sample Median

To calculate the median, the values should firstly be arranged in ascending order. Then, median can be calculated depending on whether the number of observations is odd or even. If it's odd, the median is the middle number, if it's even, median is the average of the two middle numbers. However, in our case, we have 12 values, which is even. So, after arranging the numbers in ascending order you get: 7.6, 8.3, 9.3, 9.4, 9.4, 9.7, 10.4, 11.5, 11.9, 15.2, 16.2, and 20.4. Then, the median would be the mean of the 6th and 7th numbers (9.7 and 10.4). Here's how to do it: \n\n \[ \text{{median}} = \frac{{9.7+10.4}}{2} \]
03

Comparison of Mean and Median

Compare the values of the mean and median. If the mean and median are similar, the data is likely symmetrical. If they're noticeably different, like in this case, it indicates a skew in the data. One of the reasons they're different might be due to the presence of outliers in the data. The mean is more sensitive to extreme values compared to the median, making it less representative when there are anomalies present. Thus, in this scenario, the median could be regarded as more representative for the transferrin receptor concentration in the sample.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Descriptive Statistics
Descriptive statistics is a branch of statistics that involves the organization, summarization, and display of data. This includes the use of tables, charts, and numerical measures such as mean and median. Descriptive statistics provide a way to describe the basic features of data and allow for a more comprehensive understanding by simplifying large amounts of data into a few summary indicators.

For example, in studying iron deficiency during pregnancy, descriptive statistics enable researchers to summarize transferrin receptor concentration levels from a group of pregnant women into meaningful figures that can be quickly understood and communicated.
Central Tendency
Central tendency refers to measures that identify the center of a data set and include the mean, median, and mode. These measures highlight where most of the data points cluster. In the context of the problem, we calculated the sample mean and median, which are two of the most common measures of central tendency.

The mean is simply the average, obtained by summing up all values and dividing by the count. The median indicates the middle value of the sorted list and offers a better reflection of the central location when the data contains outliers or is skewed. Understanding both helps to compare different aspects of the central tendency of data related to medical conditions like iron deficiency in pregnancy.
Statistical Measures for Data Analysis
Statistical measures are essential tools for data analysis, providing a means to interpret and derive meanings from data sets. Among these measures, the mean and median are particularly important. The mean offers a simple interpretation of the average value, but can be misleading if the data set contains extreme values or outliers. On the other hand, the median provides a more robust measure that is less sensitive to such anomalies.

These measures help us analyze and interpret data on health-related topics, like iron deficiency, providing insights that can guide medical practitioners and policymakers in decision-making and in understanding the prevalence and intensity of various health conditions.
Iron Deficiency in Pregnancy
Iron deficiency in pregnancy is a significant health concern, as it may lead to anemia and other complications for both the mother and the fetus. Understanding iron levels through descriptive statistics aids in creating a clearer picture of iron deficiency in a given population. In this context, transferrin receptor concentrations are studied to assess iron status. The sample mean may be more influenced by extreme values whereas the median provides a more accurate reflection of a typical case, which is crucial for making informed decisions on supplemental iron requirements and for evaluating the effectiveness of health interventions.

By applying the concepts of central tendency and other statistical measures to such medical data, we not only gain a deeper understanding of the conditions but also contribute to improving public health outcomes.

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Most popular questions from this chapter

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