Answer:
a) Proportion of the sampled angles are at least 30° = 0.144
b) Proportion of sampled angles between 10 and 25 = 0.415
Step-by-step explanation:
Class Relative Frequency
0-<5 0.176
5-<10 0.169
10-<15 0.179
15-<20 0.139
20-<30 0.193
30-<40 0.075
40-<60 0.04
60-<90 0.029
A) Proportion of the sampled angles which are at least 30° can be calculated by adding the relative frequencies which are greater than 30. This will include the classes 30-<40, 40-<60 and 60-<90, So,
proportion of the sampled angles are at least 30° = 0.075 + 0.04 + 0.029
proportion of the sampled angles are at least 30° = 0.144
B) For the proportion of angles between 10 and 25, we need to consider the classes 10-<15, 15-<20 and 20-<30. Since we are interested in the angles up till 25 degrees, we need to divide the relative frequency of the class 20-<30 by 2 because 25 lies in the middle of this class. So,
Proportion of sampled angles between 10 and 25 = 0.179 + 0.139 + (0.193/2)
Proportion of sampled angles between 10 and 25 = 0.415
C) For constructing the histogram, you need to plot the relative frequencies on the y axis and the classes on the x-axis by choosing a suitable scale for both the axes. I have plotted the graph on paint but its a bit untidy. I am attaching the graph as a snippet here so that you can have an idea of the heights.
By looking at the heights of the classes, we can say that <u>The distribution of misorientation angles is heavily positively skewed</u> because there is a tail at the positive side of the graph. The graph is also unimodal since there is only one highest peak present.
