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LBSRE1021 Lecture 6

LBSRE1021 Lecture 6. The Normal Distribution. Normal Distribution. Many variables are Normally Distributed Very important in Sampling theory Symmetrical (Mean = Median = Mode) Bell shaped Continuous. Example Data (Frequency distribution). Histogram. Frequency Polygon.

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LBSRE1021 Lecture 6

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  1. LBSRE1021 Lecture 6 The Normal Distribution

  2. Normal Distribution • Many variables are Normally Distributed • Very important in Sampling theory • Symmetrical (Mean = Median = Mode) • Bell shaped • Continuous

  3. Example Data (Frequency distribution)

  4. Histogram

  5. Frequency Polygon

  6. Normal Distribution Curve The mean and Standard Deviation describe the central tendency and spread of data Mean (Mode and Median same if symmetrical) Spread

  7. Central Tendency Same Location Measure, Different Dispersion Measure

  8. Z Scores A population has a mean u and standard deviation ó For a value x (on the x axis) Z = x - u ó I.e Z is the number of standard deviations x is away from the mean.

  9. Central Tendency Nearly all data are within mean ± 3 standard deviations Mean -3 sd -2 sd -1 sd +1 sd +2 sd +3 sd

  10. Central Tendency Proportions of Curve

  11. Use of Z scores • Can PREDICT the proportion of a normal distribution that is more than, or less than, a certain measurement. • To do this we use Z score TABLE (see textbook).

  12. Z Score Table

  13. Use Z Score to find proportion

  14. Application of Z score

  15. Application of Z Scores

  16. Application of Z Scores

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