Statistics Chapter 6

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Central Limit Theorem

As the sample size (n) increase without limit, the shape of the distribution of the sample means (WITH REPLACEMENT) from a population with a mean and standard deviation will approach a “normal” deviation and will have a mean and standard deviation.

z-score DEFINITION

The number of standard deviations above or below the mean the data is located

individual z-score EQUATION

(x-mean) **/** standard deviation

sample z-score EQUATION

(x-mean) **/** (standard deviation/square root of sample size)

5 Properties of a “Normal Distribution”

1. Mean=Median=Mode
2. Symmetrical and Unimodal (“Bell-shaped”)
3. Continuous and Never Touches X-axis
4. Area Under Curve (or, Probability) = 1
5. 1 SD=68%, 2 SDs=95%, 3 SDs=99.7%

Mean of a NORMAL Distribution

0

SD of a NORMAL Distribution

1

Sampling Error

Polled data will not PERFECTLY reflect entire data

Sampling Distribution of Mean

1. The mean of many samples is closer to the actual mean than the mean of one sample
2. Distribution is close together

Continuity Correction

*(if applicable to specific problem)* . When solving for x, actually solve for a range above and below x by 0.5.

\
ex.

9\.5

Mean/Median/Mode for LEFT-SKEWED data?

Mean