To determine how many points lie above the line y = x on the QQ-plot, we need to compare the ordered values of the data set S with the ordered quantiles of the uniform distribution.
First, let's sort the values in S in ascending order:
S = {0.01, 0.1, 0.2, 0.28, 0.8}
Now, let's determine the quantiles of the uniform distribution. Since we are dealing with five values, we can assign each value to a quantile based on its position:
0.01 -> 0.2
0.1 -> 0.4
0.2 -> 0.6
0.28 -> 0.8
0.8 -> 1.0
Now, plotting the points (x_i, quantile) on the QQ-plot, we find:
(0.01, 0.2)
(0.1, 0.4)
(0.2, 0.6)
(0.28, 0.8)
(0.8, 1.0)
Examining the points on the plot, we can see that all five points lie above the line y = x. Therefore, the answer is that all points in the QQ-plot lie above the line y = x.
The problems on this page concern the data set
S = \{ 0.28, 0.2, 0.01, 0.80, 0.1 \} .
Let x_ i denote the i'th element of the data set S.
Consider the QQ-plot of the data set S against the distribution \text {Unif}(0,1). (You may graph the plot using computational tools.)
How many points in the QQ-plot lie above the line y = x?
1 answer
1 answer