# The accompanying summary data on CeO2 particle sizes (nm)

Chapter 1, Problem 12E

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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).

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).

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

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