Quantitative data represents
measurable characteristics such as height, age, income etc. by numbers
or count of units. Because such data has numerical meaning, it can be
summarised in more ways than is possible with qualitative data. The most common
way to summarise quantitative
data set is to describe where the "center" is that represents a typical value. The center of a data set
can
be measured in different ways, and the method chosen can greatly influence the conclusions about the
data.[1,p.75]Mean, also referred to as "average" is the most common
statistic used to measure the center, or
middle of a numerical data set. The mean is
calculated as the sum of all the numbers divided by the total count
of numbers. The mean of a sample is called the sample mean and is
denoted by latin letter "x̄" with a macron over it, pronounced as
"ex bar".[7] The formula to finding the sample mean is:[1,p.76]
$$\overline x = {{\sum {{x_i}} } \over n}$$
Where, x = each value in the data set i = the counter of the values in the data set, from 1 to n n = the total number of values in the data set
The mean of the entire population is called the population
mean, and it is denoted by Greek letter "μ", pronounced as "mu".[1,p.54,76][2] It is found by summing up all the values in the population and dividing
by population
size, which is denoted by capital Latin letter "N". Typically, the population mean is unknown and sample
mean is used
to estimate it, plus or minus margin of
error
.[1,p.76]
The mean may not be a fair representation of the data, because the average is
easily influenced by outliers.[1,p.56]Outliers in a quantitative data set are numbers that are extremely
high or extremely low compared to the
rest of the data.[1,p.77] Like the exact balancing point of a seesaw is affected by the weight of
the people
on each
side, not by the number of people of each side, the mean is affected by the actual values of the data, rather
than the amount of data.[1,p.113]
In a skewed data set outliers will "attract" the
mean, i.e. the mean will be closer
to the outliers than the median. Because of the way mean is calculated, high
outliers tend to drive the mean upward, and low outliers tend to
drive mean downwards.[1,p.77]