Common Challenge
or Misconception
1. Population
Distribution
and
Distribution of
sample means
are different.
2. Discrete and
Continuous
Variable
Graphs can be
confused.
What it looks like
How to Help
Sometimes we can see normal distribution in both population
and sample distributions. However as shown in figure 4.4
distribution of sample means are different from population
distribution.
Explanation:
Population
distribution is a
parameter. It does not
need to show a normal
distribution. However,
if we select any
sample from this
population the means
of these samples show
a normal distribution.
Sometimes discrete variable graphs can be shown as continuous
variable graphs.
By giving examples to
each variable can
eliminate
misconceptions.
Discrete
Variable:The number
of books you check
out from the library.
(you can count)
3. The formulas We use different formulas because there is a difference between
for Population population standard deviation and sample standard deviation
called standard error.
standard
deviation and
sample
standard
deviation are
not the same.
Continuous
Variable:
Temperature
(you can measure)
The population
standard deviation is a
parameter, which is a
fixed value calculated
from every individual
in the population. A
sample standard
deviation is a statistic.
This means that it is
calculated from only
some of the
individuals in a
population.