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For a sample of data, I got that the mean = 4.31 and the median = 4.42. Also, 36% of the values from the sample are less than the mean. Does this illustrate that the data is skewed left?

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  • $\begingroup$ I would say "indicate" rather than "illustrate", though it may depend on your definition of skewness $\endgroup$ – Henry Sep 15 '15 at 9:15
  • $\begingroup$ Also, I found 4 outliers from a method using mean and standard deviation and 5 outliers (4 were the same as before) from a method using quartiles. Does this indicate that these outliers are not significant? $\endgroup$ – Will Sep 15 '15 at 9:17
  • $\begingroup$ Outliers is a different question: with mechanical identification it will depend on the underlying distribution and on sample size. $\endgroup$ – Henry Sep 15 '15 at 9:32
  • $\begingroup$ Can you help me understand this? $\endgroup$ – Will Sep 15 '15 at 10:10
  • $\begingroup$ 4.37 4.56 4.26 4.56 4.3 4.46 3.84 4.57 4.26 4.37 3.49 4.43 4.48 4.01 4.29 4.42 4.23 4.42 4.23 3.49 4.29 4.29 4.42 4.49 4.38 4.42 4.29 4.38 4.22 3.48 4.38 4.56 4.45 3.49 4.23 4.62 4.53 4.45 4.53 4.43 4.38 4.45 4.5 4.45 4.55 4.45 4.42 $\endgroup$ – Will Sep 15 '15 at 10:10
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Here is a histogram illustrating your data.

histogram

As you surmised from the summary statistics, this data distribution is left skewed and most of that skewness is caused by the four observations between $3.4$ and $3.5$. Whether they or any others are faulty observations or not is for you to decide, but you should be reluctant to exclude them from the analysis without good reason.

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