Page 172 - Data Science class 10
P. 172
and
s
s =
x n
Where
m = Population mean
m = Sample mean
x
s = Population standard deviation
s = Sample standard deviation
x
n = Sample size
After thoroughly understanding the central limit theorem, let's examine some of its practical applications and the
formula to calculate it, let us learn why the central limit theorem is so important. Let us have a look at the below
example of the Central Limit Theorem Formula:
The figure below illustrates a normally distributed characteristic, X, in a population in which the population mean
is 75 with a standard deviation of 8.
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40 45 50 55 60 65 70 75 80 85 90 95 100
If we take simple random samples (with replacement) text annotation indicator of size n=10 from the population
and compute the mean for each of the samples, the Central Limit Theorem states that the distribution of sample
means should be approximately normal. Sampling 'with replacement' means that when a unit selected at random
from the population, it is returned to the population (replaced), and then a second element is selected at random.
Note that the sample size (n=10) is less than 30, but the source population is normally distributed, so this is not a
problem. The distribution of the sample means is illustrated below. The range is narrower, and the horizontal axis
is different from the preceding picture.
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62 64 66 68 70 72 74 76 78 80 82 84 86
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