How to tell if data is normally distributed? (2024)

FAQs

How to tell if data is normally distributed? ›

One way is to make a histogram of the data. If the shape of the distribution resembles a bell curve, the data is likely normal. Another way is to create a Q-Q plot. If the points in the plot roughly fall along a straight diagonal line, then the data is assumed to be normally distributed.

If you want to check the normal distribution using a histogram, plot the normal distribution on the histogram of your data and check that the distribution curve of the data approximately matches the normal distribution curve.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. The normal distribution appears as a "bell curve" when graphed.

Visual Normality Tests / Graphical Analysis

If you see a bell curve, a distribution is approaching normal. Tall, thin curve = smaller standard deviation. Fatter, lower curve = larger standard deviation. You can test using a Normal Probability Plot.

What is normal distribution? A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme. The middle of the range is also known as the mean of the distribution.

Visualize the data distribution using graphical methods such as histograms, density plots, box plots, and quantile-quantile (Q-Q) plots. Histograms provide a visual representation of the frequency distribution by dividing the data into intervals or bins and plotting the number of observations within each bin.

In some cases, this can be corrected by transforming the data via calculating the square root of the observations. Alternately, the distribution may be exponential, but may look normal if the observations are transformed by taking the natural logarithm of the values. Data with this distribution is called log-normal.

The two well-known tests of normality, namely, the Kolmogorov–Smirnov test and the Shapiro–Wilk test are most widely used methods to test the normality of the data. Normality tests can be conducted in the statistical software “SPSS” (analyze → descriptive statistics → explore → plots → normality plots with tests).

If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size. For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μX=μ and standard deviation σX=σ/√n, where n is the sample size.

Characteristics of Normal Distribution

Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A normal distribution is perfectly symmetrical around its center. That is, the right side of the center is a mirror image of the left side.

What does normally distributed data look like? ›

In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center.

If your data is not normal, you may try to transform or normalize it to make it more normal. Transformation is the process of applying a mathematical function to your data, such as log, square root, or inverse, to change its shape and reduce its skewness or outliers.

The most commonly used method is the histogram. Plotting a histogram of the variable of interest will give an indication of the shape of the distribution and is the most commonly used. A normal approximation curve can also be added by editing the graph.

In order to determine normality graphically, we can use the output of a normal Q-Q Plot. If the data are normally distributed, the data points will be close to the diagonal line. If the data points stray from the line in an obvious non-linear fashion, the data are not normally distributed.

The most common graphical tool for assessing normality is the Q-Q plot. In these plots, the observed data is plotted against the expected quantiles of a normal distribution. It takes practice to read these plots. In theory, sampled data from a normal distribution would fall along the dotted line.

A normal distribution is symmetrical around the mean. Normal distribution reaches its highest point at the mean. It is bell-shaped. It has a zero point at the mean and it decreases as you move away from the mean on both sides.

The most commonly used method is the histogram. Plotting a histogram of the variable of interest will give an indication of the shape of the distribution and is the most commonly used. A normal approximation curve can also be added by editing the graph.

Let X be a continuous random variable. Then X takes on a standard normal distribution if its probability density function is f(x)=1√2πexp(−12x2). f ( x ) = 1 2 π e x p ( − 1 2 x 2 ) . In other words, the standard normal distribution is the normal distribution with mean μ=0 and standard deviation σ=1 .

The Central Limit Theorem says that no matter what the distribution of the population is, as long as the sample is “large,” meaning of size 30 or more, the sample mean is approximately normally distributed.

The histogram and the normal probability plot are used to check whether or not it is reasonable to assume that the random errors inherent in the process have been drawn from a normal distribution. The normality assumption is needed for the error rates we are willing to accept when making decisions about the process.