Figure 1 Normal distributions differing in mean and standard

Figure 1. Normal distributions differing in mean and standard deviation.

1. The graph above is from the source provided in Module 3 about normal distributions. All three lines represent a normal distribution, but the means and standard deviations differ for each. Explain how the means and standard deviations differ for each distribution (black, red and green), and give an example of a data set that would be appropriate for each.

Solution

The mean of distribution with green graph has mean lesser than as compared to red which in turn has mean less than black, which is evident from the graph.

Also the scatteredness in black is more than as compared to red which in turn as more scatterdness as compared to green.

So we can say that

mean and standard deviation of green distribution< mean and standard deviation of red distribution < mean and standard deviation of black distribution