Solution Found!
The accompanying summary data on CeO2 particle sizes (nm)
Chapter 1, Problem 12E(choose chapter or problem)
Problem 12E
The accompanying summary data on CeO2 particle sizes (nm) under certain experimental conditions was read from a graph in the article "Nanoceria—Energetics of Surfaces, Interfaces and Water Adsorption" (J. of the Amer. Ceramic Soc., 2011: 3992-3999):
a. What proportion of the observations are less than 5?
b. What proportion of the observations are at least 6?
c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular, does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? [Note: The investigators fit a lognormal distribution to the data; this is dis-cussed in Chapter 4.]
d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).
Questions & Answers
QUESTION:
Problem 12E
The accompanying summary data on CeO2 particle sizes (nm) under certain experimental conditions was read from a graph in the article "Nanoceria—Energetics of Surfaces, Interfaces and Water Adsorption" (J. of the Amer. Ceramic Soc., 2011: 3992-3999):
a. What proportion of the observations are less than 5?
b. What proportion of the observations are at least 6?
c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular, does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? [Note: The investigators fit a lognormal distribution to the data; this is dis-cussed in Chapter 4.]
d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).
ANSWER:
Answer
Step 1 of 5
From the given data find relative frequencies and densities
values |
frequency |
Relative frequencies |
Frequency density |
3.0-<3.5 |
5 |
5/131=0.038 |
5/5=1 |
3.5-<4.0 |
15 |
15/131=0.115 |
15/5=3 |
4.0-<4.5 |
27 |
27/131=0.206 |
27/5=5.4 |
4.5-<5.0 |
34 |
34/131=0.26 |
34/5=6.8 |
5.0-<5.5 |
22 |
22/131=0.168 |
22/5=4.4 |
5.5-<6.0 |
14 |
14/131=0.107 |
14/5=2.8 |
6.0-<6.5 |
7 |
7/131=0.053 |
7/5=1.4 |
6.5-<7.0 |
2 |
2/131=0.015 |
⅖=0.4 |
7.0-<7.5 |
4 |
4/131=0.031 |
⅘=0.8 |
7.5-<8.0 |
1 |
1/131=0.008 |
⅕=0.2 |
total |
131 |
1 |