Question

A statistician received some data to analyze. The sender of the data suggested that the data was normally distributed. Which of the following methods can be used to determine if the data is, in fact, normally distributed? O Compute the intervals x – bar #s, X – bar + 2s, and x – bar = 3s and determine the percentage of measurements falling in each. Compare these percentages to 68%, 95%, and 100%.

O Calculate a value of IQR. If this value is approximately 1.3, then the data is normal.
o Construct a normal probability plot of the data. If the points fall on a straight line, then the data is normal.
O Construct a histrogram and/or stem-and-leaf display of the data and check the shape.
O All of these could do this.

Answer 1

All of these could do this.

Explanation:

Normal distribution is a form of probability distribution that is symmetric about the mean, to depict data near the mean are more frequent in occurrence than data far from the mean. Normality of data can be measured by either power or the Shapiro-Wilk test.

Some ways of testing the normal distribution of data are by:

i. Histogram, which is a data visualization that shows the distribution of plotted sample data. The frequency of occurrence per value in the data set determines its distribution.

ii. Interpretation of the shape.

iii. Probability plot of the data, e.g Box Plot, QQ Plot etc. If the dots fall exactly on the black line, then a given sample of data are normal. If not, otherwise.

iv. Calculating interquartile range (IQR), which is a measure of variability. Sample of data are normally distributed when the interquartile range (IQR) is 1.34896.

Therefore, all the given methods could be used to determine if the data is normally distributed.