Chapter 3 Descriptive Statistics
3.1 Describing Central Tendency
Mean.
Mean is a measure of central location computed by summing the data values and dividing by the
number of observations.
Sample Mean:
Population Mean:
Where:
n = number of elements (observations) in a
sample
Where:
N = number of elements (observations) in a
population.
For example: Given the data values: 46, 54, 42, 46, and 32. Get the Sample Mean.
n = 5.
Then,
Sample mean is a point estimator of the population mean.
In Excel: =AVERAGE(RANGE)
Median
.
Median is a measure of central location provided by the value in the middle when the data are
arranged in ascending order.
First, Arrange the data in ascending order
a)
for an odd number of observations, the median is the middle value
b)
for an even number of observations, the median is the average of the two middle values
Example a):
46, 54, 42, 46, and 32.
Arrange in ascending order: 32, 42, 46, 46, 54
n = 5 (odd), then:
Median = 46
Example b):
46, 54, 42, 46, 32, and 16.
Arrange in ascending order: 16, 32, 42, 46, 46, 54
n = 5 (even), then:
Median = (42+46)/2 = 44.
Median is preferred when data contains outliers (extreme small or large values)
In Excel: =MEDIAN(RANGE)
Mode
Mode is a measure of location, defined as the value that occurs with greatest frequency.
Example:
Given the data values: 46, 54, 42, 46, 32, and 16. Get the Mode.
Arrange in ascending order: 16, 32, 42, 46, 46, 54
Class
Frequency
16
1
32
1
42
1
46
2
54
1
The Mode, or the class with highest frequency, is 46.
In Excel: =MODE(RANGE)
3.2 Measures of Variation