A river starts in a massive and beautiful lake. Then it flows through prime trout fishing areas to a famous waterfall. After it leaves the park, the river is an important source of water for wildlife, ranchers, farmers, and cities downstream. How much water does leave the park each year? The annual flow of the river (units 108 cubic meters) is shown here for 19 recent years. 25.9 32.4 33.1 19.1 17.5 24.9 21.0 45.1 30.8 34.3 27.1 29.1 25.6 31.7 23.4 24.1 23.9 25.9 18.6 (a) Is there a "guaranteed" amount of water farmers, ranchers, and cities will get from the river each year? Yes, flows occur at the same rate at corresponding times throughout the year.Yes, flows occur at a constant rate. No, annual flows are a random variable.Yes, flows average out to the same value across each year.No, annual flows change at a steady rate from year to year. (b) What is the "expected" annual flow from the snowmelt? Find the mean, median, and mode. (Round your answers to two decimal places.) mean median mode (c) Find the range and standard deviation of annual flow. (Round your answers to two decimal places.) range standard deviation
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In the Western United States there is a saying, "Whisky is for drinken but water is for fighten!" Water and water rights have been fought over ever since ranchers and settlers moved into Wyoming, Montana, and the West. Even today farmers and ranchers fight cities and large developments over water from snowmelt that originates deep in the Rocky Mountains.
A river starts in a massive and beautiful lake. Then it flows through prime trout fishing areas to a famous waterfall. After it leaves the park, the river is an important source of water for wildlife, ranchers, farmers, and cities downstream. How much water does leave the park each year? The annual flow of the river (units 108 cubic meters) is shown here for 19 recent years.
| 25.9 | 32.4 | 33.1 | 19.1 | 17.5 | 24.9 | 21.0 | 45.1 | 30.8 | 34.3 |
| 27.1 | 29.1 | 25.6 | 31.7 | 23.4 | 24.1 | 23.9 | 25.9 | 18.6 |
(b) What is the "expected" annual flow from the snowmelt? Find the mean, median, and
| mean | |
| median | |
| mode |
(c) Find the
| range | |
| standard deviation |
(d) Find a 75% Chebyshev interval around the mean. (Round your answers to two decimal places.)
| Lower Limit | |
| Upper Limit |
(e) Give a five-number summary of annual water flow from the river.
| min | Q1 | median | Q3 | max |
Make a box-and-whisker plot.
Interpret the five-number summary and the box-and-whisker plot. Where does the middle portion of the data lie?
What is the interquartile range?
Can you find data outliers? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
(f) Another river is a smaller but very important source of water flowing out of the park from a different drainage. Ten recent years of annual water flow data are shown below (units 108 cubic meters).
| 3.83 | 3.81 | 4.01 | 4.84 | 5.81 | 5.50 | 4.31 | 5.81 | 4.31 | 4.47 |
| original river's coefficient of variation | |
| smaller river's coefficient of variation |
What do you conclude?
(g) Based on the data, would it be safe to allocate at least 31 units of the orginal river water each year for agricultural and domestic use? Why or why not?
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