3C Histograms. Sample answer: The least value in the data is 1 and the greatest is 1,135. An interval of 200 would yield the frequency table below.
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1 POPULATION The list gives the approximate population density for each state. Choose intervals and make a frequency table. Then construct a histogram to represent the data. Sample answer: The least value in the data is 1 and the greatest is 1,135. An interval of 200 would yield the frequency table below. Show the intervals from the frequency table on the horizontal axis of the histogram. Show the frequency on the vertical axis. esolutions Manual - Powered by Cognero Page 1
2 VOLCANOES Use the histogram below. a. What percent of the volcanoes are 8,999 feet or less? b. How likely is it that any given volcano is at least 15,000 feet tall? Explain your reasoning. c. What is the height of the tallest volcano? a. There are or 15 volcanoes that are 8,999 feet or less. There are or 25 volcanoes in all. So, 60% of the volcanoes are 8,999 feet or less. b. Look at the graph. There are or 2 volcanoes that are at least 15,000 feet tall, and there are 25 volcanoes in all. It is not very likely that any given volcano is 15,000 feet or taller. Sample reasoning: Only two volcanoes out of 25 are 15,000 feet or taller. c. The height of the tallest volcano cannot be determined from the data presented in the graph because actual heights are not given. We only know that the height of the tallest volcano is in the interval 18,000 20,999 feet. esolutions Manual - Powered by Cognero Page 2
3 Choose intervals and make a frequency table. Then construct a histogram to represent the data. Sample answer: The least value in the data is 0 and the greatest is 14. An interval of 3 would yield the frequency table below. Show the intervals from the frequency table on the horizontal axis of the histogram. Show the frequency on the vertical axis. Sample answer: The least value in the data is 0.17 and the greatest is 200. An interval of 20 would yield the frequency table below. esolutions Manual - Powered by Cognero Page 3
4 frequency table below. Show the intervals from the frequency table on the horizontal axis of the histogram. Show the frequency on the vertical axis. esolutions Manual - Powered by Cognero Page 4
5 COUNTRIES Use the histogram shown. a. How many countries have an area less than 401 square kilometers? b. What percent of the countries have an area of square kilometers? c. How likely is it that any given country will have an area greater than 800 square kilometers? Explain. a. There are or 30 countries that have an area less than 401 square kilometers. b. There are or 19 countries with an area of square kilometers. There are or 50 countries in all. So, 38% of the countries have an area of square kilometers. c. There are or 4 countries that have an area greater than 800 square kilometers, and there are 50 countries in all. It is not very likely that any given country will have an area greater than 800 square kilometers. esolutions Manual - Powered by Cognero Page 5
6 ECLIPSES Use the histogram shown. a. What percent of the solar eclipses lasted at least 7 minutes 31 seconds? b. How long was the shortest solar eclipse? c. What is the duration of a typical solar eclipse during the decade? Explain your reasoning. d. How many solar eclipses lasted between 1 second and 5 minutes? a. There were or 2 solar eclipses that lasted at least 7 minutes 31 seconds. There were or 16 solar eclipses in all. So, 12.5% of the solar eclipses lasted at least 7 minutes 31 seconds. b. Sample answer: The shortest solar eclipse cannot be determined from the data presented in the graph because actual times are not given. We only know that the shortest solar eclipse is in the interval 0:01 2:30 seconds. c. Sample answer: There were solar eclipses that lasted from 1 second to five minutes. There were or 5 solar eclipses that lasted from 5 minutes 1 second to 12 minutes 30 seconds. So, a typical solar eclipse lasted from 1 second to 5 minutes. d. There were or 11 solar eclipses that lasted between 1 second and 5 minutes. esolutions Manual - Powered by Cognero Page 6
7 BUILDINGS Use the histograms shown. a. Which city has the tallest building? b. Determine which city has more buildings that are feet tall. c. Determine which city has more buildings that are at least 600 feet tall. What percent of the buildings in that city are at least 600 feet tall? d. Which city has more tall buildings? by how many? a. The tallest building in Seattle is in the interval feet, and the tallest building in Pittsburgh is in the interval feet. So, Seattle has the tallest building. b. Pittsburgh has 1 building in the interval feet, and Seattle has no buildings in this interval. So, Pittsburgh has more buildings that are feet tall. c. Pittsburgh has or 5 buildings that are at least 600 feet tall, and Seattle has or 7 buildings that are at least 600 feet tall. So, Seattle has more buildings that are at least 600 feet tall. Seattle has or 21 buildings in all. So, about 33% of Seattle s buildings are at least 600 feet tall. d. Pittsburgh has or 15 tall buildings, and Seattle has 21 tall buildings. So, Seattle has or 6 more tall buildings than Pittsburgh has. esolutions Manual - Powered by Cognero Page 7
8 WALKING The table shows the number of minutes Penny waked her dog each day this month. What fraction of the days did she walk her dog 12 minutes or less? Write in simplest form. Find the cumulative relative frequency. There were or 30 days and or 16 days that she walked her dog for 12 minutes or less. So, or of the days she walked her dog for 12 minutes or less. What fraction of the days did she walk her dog less than 16 minutes? Write in simplest form. Find the cumulative relative frequency. There were or 30 days and or 20 days that she walked her dog for less than 16 minutes. So, or of the days she walked her dog for less than 16 minutes. esolutions Manual - Powered by Cognero Page 8
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