1.3 Central Tendency

Biostatistics for the Clinician

Biostatistics for the Clinician

University of Texas-Houston
Health Science Center

Lesson 1.3

Central Tendency

Lesson 1: Summary Measures of Data 1.3 - 1

Biostatistics for the Clinician

1.3 Central Tendency

1.3.1 Why Important
Why do you need to know about measures of central tendency? You need to be able to understand how the locations of large amounts of data can be summarized using simple measures to best represent the the data as a whole. Why? Because these kind of summary values, occur again and again in the medical research literature. You cannot understand, let alone critically evaluate medical research studies unless you understand the appropriate usage of such measures.

Central Tendency
Practice
Exercise 1: You need to understand the measures of central tendency to:
No Response
Know biostatistical vocabulary
Compute statistics
Evaluate medical research studies
None of the above

Lesson 1: Summary Measures of Data 1.3 - 2

Biostatistics for the Clinician
Collectively, the measures of location are referred to as measures of central tendency. Measures of central tendency are ubiquitous throughout the medical research literature. There are many of them. But, by far the most important and frequently used are the mean, the median, and the mode (see Figure 2.3 below).

Figure 2.3: Measures of Central Tendency

Graphs are frequently used in biostatistics to represent, and view as a whole, large amounts of data. Figure 2.3 might display a graph of physicians salaries in 1999 after federal health plans have come forward, but it's old data actually. The point of the graph is to show you that there are various ways to represent a distribution of data. The mean is the average value. The median has equal numbers of values both above and below it. The mode is the most frequent value in the distribution. It turns out that if the distribution is a nice symmetric distribution, (that is, the left half is the mirror image of the right half of the curve) all three have the same value.

Central Tendency
Practice
Exercise 2: Central tendency is measured by:
No Response
The Mean
The Median
The Mode
All except "No Response" above

Lesson 1: Summary Measures of Data 1.3 - 3

Biostatistics for the Clinician

1.3.2 Mean
The most frequently used measure of central tendency is the mean. The mean, or more formally, the arithmetic mean, is simply the average of the group. That is, the mean is obtained by summing all the numbers for the subjects in the group and dividing by the number of subjects in the group. The mean is useful only for quantitative variables (see Figure 2.3).

Central Tendency
Practice
Exercise 3: The mean (or arithmetic mean) is the:
No Response
Average
Middle value
Most frequent value
Highest value

Lesson 1: Summary Measures of Data 1.3 - 4

Biostatistics for the Clinician

1.3.3 Median
The median is the middle score. That is, the median is the score for which half the subjects have lower scores and half have higher scores. Another way to say this is that the median is the score at the fiftieth percentile in the distribution of scores (see Figure 2.3).

Central Tendency
Practice
Exercise 4: The median is the:
No Response
Average
Middle value
Most frequent value
Highest value

Lesson 1: Summary Measures of Data 1.3 - 5

Biostatistics for the Clinician

1.3.4 Mode
The mode is the most frequent score. Another way to say this is that the mode is the score that occurs most often (see Figure 2.3).

Central Tendency
Practice
Exercise 5: The mode is the:
No Response
Average
Middle value
Most frequent value
Highest value

Lesson 1: Summary Measures of Data 1.3 - 6

Biostatistics for the Clinician

1.3.5 Summary Principle
In a symmetric distribution with one mode like the Gaussian or normal distribution the mean, median and mode all have the same value. But, in a non-symmetric distribution their values will be different. In general, as the distribution becomes more lopsided (skewed) the mean and the median move away from the mode. With extremely skewed distributions the mean will be somewhat misleading as a measure of central tendency, because it is heavily influenced by extreme scores. So for example, if you take a distribution of doctor's incomes, some doctors make huge sums of money, and the median or the mode is more representative of doctor's incomes as a whole than the mean, because the very high incomes of some doctors inflate the average, making it less representative of doctors as a whole (see Figure 2.3). Keep in mind, as was discussed in the section on levels of measure, it is not appropriate to compute means unless distributions consist of interval or ratio data.

Central Tendency
Practice
Exercise 6: Which measure of central tendency is most appropriate depends upon the:
No Response
Average
Middle value
Most frequent value
Kind of distribution

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Central Tendency

Lesson 1: Summary Measures of Data 1.3 - 7