1. Chapter 5
A Normal World

2. GED111/CDS111 Statistics in Modern Society
What is Normal?
The Normal Distribution
Single peaked
Symmetric
Same point for mean, median, mode
Bell/mourn shape
Variation can be characterized by the standard deviation
GED111/CDS111 Statistics in Modern Society

3. The Normal Distribution and Relative Frequencies
The relative frequency for any range of data values is the area under the curve covering that range of values
The total relative frequency for any data set must be 1, thus the total area under the normal distribution curve must equal 1
GED111/CDS111 Statistics in Modern Society

4. When Can We Expect a Normal Distribution?
Most data values are clustered near the mean, giving the distribution a well-defined single peak
Data values are spread evenly around the mean, making the distribution symmetric
Larger deviations from the mean become increasingly rare, producing the tapering tails of the distribution
Individual data values result from a combination of many different factors, such as genetic and environmental factors
GED111/CDS111 Statistics in Modern Society

5. GED111/CDS111 Statistics in Modern Society
Exercises
Q11-18 p202
GED111/CDS111 Statistics in Modern Society

6. Properties of the Normal Distribution
About 68% of the data points fall within 1 standard deviation of the mean
About 95% of the data points fall within 2 standard deviations of the mean
About 99.7% of the data points fall within 3 standard deviations of the mean
GED111/CDS111 Statistics in Modern Society

7. GED111/CDS111 Statistics in Modern Society
Applying the Rule
Guideline can be set to distinguish “unusual” values
GED111/CDS111 Statistics in Modern Society

8. GED111/CDS111 Statistics in Modern Society
Standard Scores
The number of standard deviations a data value lies above or below the mean
GED111/CDS111 Statistics in Modern Society

9. Standard Scores and Percentiles
Standard scores can be converted to percentiles
Table 5.1 p211
Percentage, relative frequency, proportion, probability
GED111/CDS111 Statistics in Modern Society

10. The Central Limit Theorem
Suppose we take many random samples of size n for a variable with any distribution (not necessarily a normal distribution) and record the distribution of the means of each sample
The distribution of the means will be approximately a normal distribution for large sample sizes
The mean of the distribution of means approaches the population mean, µ, for large samples sizes
The standard deviation of the distribution of means approaches σ/√n for large sample sizes, where σ is the standard deviation of the population
GED111/CDS111 Statistics in Modern Society

11. The Central Limit Theorem (cont.)
Figure 5.26 p218
Software
GED111/CDS111 Statistics in Modern Society

12. GED111/CDS111 Statistics in Modern Society
Focus on Psychology
Are We Smarter Than Our Parents? p229
GED111/CDS111 Statistics in Modern Society