How To Determine If Data Is Approximately Normally Distributed: A Guide To Using Graphical And Numerical Evidence

Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.

Looking at a z-score normal probability chart. If the graph is not linear and data is not evenly spread out (such as an exponential slope) it is not a normal distribution. Check if data fits within three standard deviations (use min. and max.). Check if empirical rule applies.

To determine whether a distribution of data is approximately normal, we can use both graphical and numerical evidence.

Graphical evidence:
– Histogram: A histogram of the data can give an indication of whether the data is symmetric and bell-shaped, which are characteristics of a normal distribution.
– QQ plot: A QQ plot (quantile-quantile plot) is a graphical tool for comparing the distribution of the data to a normal distribution. If the points on the QQ plot fall approximately on a straight line, it suggests that the data is approximately normally distributed.

Numerical evidence:
– Skewness and kurtosis: Skewness measures the extent to which the data is skewed to the left or right. A skewness value of zero indicates a roughly symmetrical distribution. Kurtosis measures the peakedness of the distribution. A kurtosis value of zero indicates a normal distribution.
– Shapiro-Wilk test: The Shapiro-Wilk test is a statistical test for normality. If the p-value of the test is greater than 0.05, it suggests that the data is normally distributed.

Overall, by analyzing both the graphical and numerical evidence, we can make a determination as to whether the distribution of data is approximately normal.

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