The normal distribution

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

What is the normal distribution?

normal_distribution.png

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Symmetrical

normal_distribution_with_dashed_line_in_the_middle.png

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Area = 1

Normal distribution with area underneath curve shaded.png

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Curve never hits 0

Normal distribution with arrows pointing to tails on either side.png

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Described by mean and standard deviation

Normal distribution with mean 20 and sd three.png

$$ Mean = 20 $$

$$ Standard \ Deviation = 3 $$

Normal distribution with mean 0 and sd 1.png

$$ Mean = 0 $$

$$ Standard \ Deviation = 1 $$

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Areas under the normal distribution

68% falls within one standard deviation

Normal distribution with area between plus minus one standard deviation labeled as 68 percent.png

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Areas under the normal distribution

95% falls within two standard deviations

Normal distribution with area between plus minus two standard deviation labeled as 95 percent.png

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Areas under the normal distribution

99.7% falls within three standard deviations

Normal distribution with area between plus minus three standard deviation labeled as 99.7 percent.png

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Why is the normal distribution important?

  • Lots of real-world data resembles a normal distribution.

Standard normal distribution.png

  • A normal distribution is required for many statistical tests.

gcse_scores_histogram.png

1 Data source: https://data.gov.uk/dataset/ec1efd76-d6ad-4594-9b4d-944aa4170e63/gcse-english-and-maths-results-by-ethnicity
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Skewness

positive_skewed_distribution.png

negative_skewed_distribution.png

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Kurtosis

  • Kurtosis - a way of describing the occurrence of extreme values in a distribution.
  • Three types of kurtosis
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Kurtosis

normal_distribution_with_different_peaks_and_tail_length.png

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Let's practice!

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