Data Distributions

Welcome to data distribution, here we are going to talk about central tendency. Keywords used are Mean, Median, Mode, Normal Distribution, Skewness, Kurtosis and various types of Skewness & Kurtosis.

 

The three measures to identify central tendency(main behavior): the mean, median, and mode. These measures relate in different ways to different distributions either skewed or normal. Intelligence tests can also be measured using central tendency principles as well each has a distribution. Intelligence tests also are biased in material and need regular updates.

The mean is the average score or the sum of the scores divided by the number of different scores. The median is the middle number in a set, which divides a distribution in half. The mode is the most frequent score, which shows up the most often. A distribution is the curve of scores. A skewed distribution is a curve that has a long tail in one direction and has extreme scores that change the mean. The three measures mean, median and mode under a normal distribution are all the same. Also in a positively skewed distribution, the mean is the greatest number, as to the median and mode. An intelligence test measures the abilities of a person and distributes it as a score. Under the standard, most scores are within 15 points of the mean, being 85 and 115. In two normal distributions, there can be an overlap as some people score above and below the mean between the groups. To determine if a test is biased then the scores of two groups need to be measured to see if the test is biased or not.

Source: Link

Mean, Median, Mode

How to use mean, median and mode to determine the shape of a distribution?

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Two things once often we should start using to be DS, are

  • Skewness
  • Kurtosis

Definitions

 

21

Skewness/Kurtosis

Skewness is the degree of departure from symmetry of a distribution. A positively skewed distribution has a tail which is pulled in the positive direction. A negatively skewed distribution has a tail which is pulled in the negative direction.

 

Kurtosis is the degree of peakedness of a distribution. A normal distribution is a mesokurtic distribution. A pure leptokurtic distribution has a higher peak than the normal distribution and has heavier tails. A pure platykurtic distribution has a lower peak than a normal distribution and lighter tails.

 

 

 

descriptive-statistics-41-638

 

 

Formulas:

f1-large

 

 

Normal Distribution Proportions

 

skew-normal-dist011

with 1 standard deviations distance, we cover 68.2% and with 2 standard deviations, we cover 68.2 + 27.2 = 95.4 (95%) of sample space.

Disclaimer: Images shown are not my own. Please be aware of copyrights before you re-publish contents.

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