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# 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).

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### 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 |