2.7.1.Properties of normal curve

Unit 2 - Probability distributions

2.7.1.Properties of normal curve
  • It is continuous, symmetrical and bell-shaped curve.
  • It is asymptotic. Both the tails extend to infinity, (-∞ to ∞) i.e., the tail approaches the base but never touches it.
  • The arithmetic mean, median and mode coincide.
Image1
  • The central position of the curve will be described by the mean and the spread of the curve by the standard deviation.
  • The coefficient of skewness is zero and the coefficient of kurtosis is 3
  • Mean plus or minus one standard deviation (m±s) includes 68.00 percent (68.27% to be more precise) of the total frequency or total area of the curve.
  • The area under Normal curve is always are,
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Fig. a: Area between m ±1
(ii) Mean plus or minus 1.96 standard deviation (m ±1.96) includes 95% of the total frequency.
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Fig.b: Area between m ± 1.96
(iii) Mean plus or minus 2.58 standard deviation (m ± 2.58) includes 99% of the total frequency.
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Fig.c: Area between m ± 2.58
Last modified: Saturday, 10 September 2011, 7:20 AM