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Central Limit
Theorem
Unit 1
Standard
MM4D1. Using
simulation, students will
develop the idea of the
central limit theorem.
The Central Limit Theorem States:
That even if a sample of data is not normal, the
sample means of at least 30 samples will be
normal.
 That the mean of the sample means will be the
mean of the population
 For random samples of size from a normal
population, the distribution of sample
means is normally distributed with the same
mean µ and standard deviation .
The
larger the sample size (n, the better will be
the normal approximation, even if the
population is not normal or its shape is
unknown.

Vocabulary
Normal Population: A population of values
having a normal distribution.
 Size n: Number of samples from the whole
population.
 Random Samples: A sample in which every
element in the population has an equal chance of
being selected.
 Sample Mean: Average of all the samples
 Normally Distributed: sometimes referred to
as a "bell-shaped distribution."
 Skewed Distribution: Distribution of a set of
values that deviates from a normal distribution
curve.
 Mean Symbol: µ

When data are skewed, they do not possess the
characteristics of the normal curve (distribution). The mean,
mode, and median do not fall on the same score. The mode
will still be represented by the highest point of the
distribution, but the mean will be toward the side with the
tail and the median will fall between the mode and mean.
Negative or Left Skew Distribution
Positive or Right Skew Distribution