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descriptive statistics and data representation-USMLE rx bricks
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Descriptive Statistics andData Representation
Last Updated: July 14, 2021
access_time17 min
Learning Objectives (4)
After completing this brick, you will be able to:
● Explain and graphically show measures of central tendency: mean,
median, and mode.
● 1
● Describe measures of variation: range, interquartile range, variance,
and standard deviation.
● 2
● Explain the measures used for normally distributed data and those
used for nonnormally distributed data, and explain the significance of
skew and outliers.
● 3
● Describe other graphical methods to understand a study cohort: pie
charts, box and whisker plots, dot plots, bar graphs (with confidence
intervals), and demographic tables.
● 4
CASE CONNECTION
Webix, a newly released antidepressant medication, is receiving a lot
of media attention. Commercials and magazine advertisements
enthusiastically quote a recent study that reports that Webix is highly
effective in improving depression symptoms. Your patient asks you if
this medication would be good for her 89-year-old mother who
,suffers from long-standing depression and who also has chronic
kidney disease and dementia. “It sounds like a promising drug,” you
tell your patient, “but I need to look into the study a little more
carefully.”
Assuming you review the study in its entirety, where specifically
could you quickly look to see if this newly released medication would
be appropriate for and applicable to your patient’s mother? How
would you explain this to your patient? Consider your answers as you
read, and we’ll revisit at the end of the brick.
What Are Descriptive Statistics and
Graphical Representations of Data?
The first step in a study analysis is to understand the nature of the
population you are studying. This is achieved by using descriptive
statistics, which help to numerically describe the population under
study. In fact, this is the main purpose of a whole branch of study
design known as descriptive studies. In most manuscripts, the first
table comprises descriptive statistics. These data help readers
understand the sample included in the study and whether this study
,applies to their own patient population. Here, we’ll look at how these
data are presented, both in tables and in graphs.
What Are Measures of Central
Tendency?
Many studies are reported by using quantitative (numerical) variables.
Height, weight, and body temperature, which can be any value in a
range, are continuous quantitative variables, whereas the number of
daily hospital admissions is a discrete variable, as it can have only
specific values (whole numbers in this case).
So how do we summarize and represent these quantitative data? For
that, we need to start with measures of two descriptors: what is the
central tendency, which is the middle of the dataset, and what is the
variability, which is how much the data differ from the central
tendency. We’ll start with central tendency. Commonly used
measures of this include mean, median, and mode.
Mean
Mean is the measure of the central tendency you might be most
familiar with and is commonly referred to as the average. We
, calculate the mean by adding up all the given data and dividing that
by the total number data points.
For example, the weights of six randomly selected individuals are 65,
78, 50, 80, 65, and 90 kg, so mean is calculated as:
(65 + 78 + 50 + 80 + 65 + 90) = 428
428 ÷ 6 = 71.3 kg
Median
Median is the middle value in a series of numerically ordered
observations (ie, from least to greatest or from greatest to least). With
an even number of data (N), the median is the average of the two
middle values. For an odd N, median is the value that lies in the (N +
1) ÷ 2 position, or the middle number in the set. To calculate median,
we arrange the given numbers in ascending (or descending) order: 50,
65, 65, 78, 80, and 90.
Here, the total number of given values is six (an even number), so we
take the average of the third and fourth position values in the
ascending order data:
65 + 78 = 143
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