Properties and uses of the mode
Properties and uses of the mode
The mode is the easiest measure of central location to understand and explain. It is also the easiest to identify, and requires no
calculations.
To identify the mode from a data set in Analysis
• The mode is the preferred measure of central location for addressing which value is the most popular or the most
Module:
Epi Info does not have a
common. For example, the mode is used to describe which day
Mode command. Thus, the best way to identify the
of the week people most prefer to come to the influenza
vaccination clinic, or the “typical” number of doses of DPT the
mode is to create a
histogram and look for the
children in a particular community have received by their
tallest column(s).
second birthday.
Select graphs, then
• As demonstrated, a distribution can have a single mode.
choose histogram under
Graph Type.
However, a distribution has more than one mode if two or more
values tie as the most frequent values. It has no mode if no
The tallest column(s)
value appears more than once.
is(are) the mode(s).
NOTE: The Means
• The mode is used almost exclusively as a “descriptive”
command provides a mode, but only the lowest
measure. It is almost never used in statistical manipulations or
analyses.
value if a distribution has
more than one mode. • The mode is not typically affected by one or two extreme values
(outliers).
Exercise 2.3
Using the same vaccination data as in Exercise 2.2, find the mode. (If you answered Exercise 2.2, find the mode from your frequency distribution.)
Check your answers on page 2-59
Median Definition of median
The median is the middle value of a set of data that has been put into rank order. Similar to the median on a highway that divides
the road in two, the statistical median is the value that divides the
To identify the median from a data set in Analysis
data into two halves, with one half of the observations being
smaller than the median value and the other half being larger.
Module:
The median is also the 50 percentile of the distribution.
th
Click on the Means
Suppose you had the following ages in years for patients with a
command under the Statistics folder.
particular illness:
In the Means Of drop-
down box, select the
variable of interest Select Variable
The median age is 28 years, because it is the middle value, with
Click OK
two values smaller than 28 and two values larger than 28.
You should see the
list of the frequency by the variable you
Method for identifying the median
selected. Scroll down until you see the
Step 1. Arrange the observations into increasing or decreasing
Median among other
order.
data.
Step 2. Find the middle position of the distribution by using the following formula:
Middle position = (n + 1) / 2
a. If the number of observations (n) is odd, the middle position falls on a single observation.
b. If the number of observations is even, the middle position falls between two observations.
Step 3. Identify the value at the middle position.
a. If the number of observations (n) is odd and the middle position falls on a single observation, the median equals the value of that observation.
b. If the number of observations is even and the middle position falls between two observations, the median equals the average of the two values.
EXAMPLES: Identifying the Median
Example A: Odd Number of Observations
Find the median of the following incubation periods for hepatitis A: 27, 31, 15, 30, and 22 days.
Step 1. Arrange the values in ascending order.
15, 22, 27, 30, and 31 days
Step 2. Find the middle position of the distribution by using (n + 1) / 2.
Middle position = (5 + 1) / 2 = 6 / 2 = 3
Therefore, the median will be the value at the third observation.
Step 3. Identify the value at the middle position.
Third observation = 27 days
Example B: Even Number of Observations
Suppose a sixth case of hepatitis was reported. Now find the median of the following incubation periods for hepatitis A: 27, 31, 15, 30, 22 and 29 days.
Step 1. Arrange the values in ascending order.
15, 22, 27, 29, 30, and 31 days
Step 2. Find the middle position of the distribution by using (n + 1) / 2.
Middle location = 6 + 1 / 2 = 7 / 2 = 3½
Therefore, the median will be a value halfway between the values of the third and fourth observations.
Step 3. Identify the value at the middle position.
The median equals the average of the values of the third (value = 27) and fourth (value = 29) observations:
Median = (27 + 29) / 2 = 28 days
Epi Info Demonstration: Finding the Median
Question:
In the data set named SMOKE, what is the median number of cigarettes smoked per day?
Answer:
In Epi Info: Select Analyze Data. Select Read (Import). The default data set should be Sample.mdb. Under Views, scroll down to view
SMOKE, and double click, or click once and then click OK. Select Means. Then click on the down arrow beneath Means of, scroll down and select NUMCIGAR, then click OK.
The resulting output should indicate a median of 20 cigarettes smoked per day.
Your Turn: What is the median height of the participants in the smoking study? (Note: The variable is coded as
feet-inch-inch, so 5'1" is coded as 501.) [Answer: 503]