Question

What kind of graphical display can we make to determine if a distribution is approximately​ normal?

Answer 1

The normal probability plot (Chambers et al., 1983) is a graphical technique for assessing whether or not a data set is approximately normally distributed. The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line. Departures from this straight line indicate departures from normality. The normal probability plot is a special case of the probability plot.

Answer 2

Answer:

The normal probability plot, histogram, and box plot can be used to determine if a distribution is approximate normal.

Explanation:

Normal probability plot

This is a graph that plots the normal scores against the data set. If the data is normally distributed, then we obtain a straight, diagonal line by joining the plotted values. However, if the plot is skewed, then the distribution is not normal.

Histogram

It uses bars to graphically represent the data. If the distribution is normal, then the histogram turns out to be bell-shaped, that is, the height of the bars keeps decreasing as we move on either side away from the middle bar. The histogram is similar in shape to the normal distribution curve if the data is normally distributed.

Box plot

This takes the form of a box and two whiskers, showing the median, upper and lower quartiles, and the maximum and minimum values. If the data is normally distributed, the median is in the middle of the box while the whiskers are about equal distance away from it.