Question

Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information is on misorientation angle (degrees).

Class: 0−<5 5−<10 10−<15 15−<20 20−<30 30−<40 40−<60 60−<90 Rel freq: 0.176 0.169 0.179 0.139 0.193 0.075 0.040 0.029
A) What proportion of the sampled angles are at least 30°? (Round your answer to three decimal places.)
B) Roughly what proportion of angles are between 10° and 25°? (Round your answer to three decimal places.)
C) Construct a histogram. Comment on any interesting features. Select all that apply
1. There are two obvious outliers.
2. Without more precise information, we cannot tell if the data contain outliers.
3. The distribution of misorientation angles is approximately symmetric.
4. The distribution of misorientation angles is heavily negatively skewed.
5. The distribution of misorientation angles is heavily positively skewed.
6. The distribution of misorientation angles is bimodal.

Answer 1

Explanation:

From the information given:

Classes 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 0.040

60 - < 90 0.029

1

(a)

So from above; the proportion of samples that are at least 30° can be computed as:

P(at least 30°) = (0.075 + 0.040 + 0.029)

P(at least 30°) = 0.144

(b)

The proportion of angles between 10° and 25° = (0.179 + 0.139 + 0.193)

= 0.511

(c) The histogram is constructed by using the EXCEL. The step in making the histogram include;

• Insert the class and relative frequency as a data set in the excel sheet
• Select relative frequency
• choose insert
• select chart
• chose 2-D column(make sure you choose the first option)
• select bars and tap format series, then adjust the gaps.

From the histogram, the chart doesn't show an outlier. The relative frequency is not also symmetrically distributed relating to the class due to the fact that the histogram does not possess a bell shape curve. Finally, we cannot determine if the distribution is positively skewed or negatively skewed because the distribution is bimodal.

6. The distribution of misorientation angles is bimodal.