# Meaning of a plot obtained by 'quantile' function of R

I have a following plot that is obtained by using the quantile function of R:

Could anyone explain me what the plot means? The input X to the quantile function QUANTILE(X, P) is a '180x100 'matrix. This function for P=95 is used on each '180x1' 100 columns yielding the '180x1' vector that denotes the 95 percent quantile pattern in the graph. In the same manner 5 percent quantile pattern is obtained. So far I have understood that the 95 percent quantile indicates that 95 percent of the values are below the 95 percent quantile pattern and 5 percent of them are below the 5 percent quantile pattern. Is this correct?I would highly appreciate suggestions.

• How was the plot obtained? What are "the values"? Jan 6 '16 at 11:04
• The input X to the quantile function QUANTILE(X, P) is a '180x100 'matrix. This function for P=95 is used on each '180x1' 100 columns yielding the '180x1' vector that denotes the 95 percent quantile pattern in the graph. In the same manner 5 percent quantile pattern is obtained.
– zsha
Jan 6 '16 at 11:36
• So what does the horizontal axis from -80 to 80 represent? Are you just asking what "quantile" means? Jan 6 '16 at 12:04
• horizontal axis represents angles while vertical axis represents the values of gain at each angle. Yes I wanted to know how to interpret this plot!
– zsha
Jan 6 '16 at 13:37

You are right: 95% quantil means that 95% of the data is lower than the quantile.

How this works for you? Take the first row, of your 180x100 matrix. Sort them. Take the 100*0.95=95th and the 100*0.05=5th value. Also calculate the mean of the other 100 values.

On your Plot the very left at $x=-90$ plot those three values. Do that for every column and connect the dots. The upper line is the represents the 95% quantile dots. The middle straight line the mean. The lower dotted line the 5% quantile. The x-axis ranges from -90 to 89 (or -89 to 90) because of your 180 rows.

This means that 90% (=95-5) of your data lies within the band of the two dotted lines.

How to interpret that? That totally depends on the underlying data.

• Now it seems clear to me. Thank you for your explanation!
– zsha
Jan 6 '16 at 13:36