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 10 8 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 8 23 1 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 average out to the same value across each year No, annual flows change at a steady rate from year to year Yes, flows occur at the same rate at corresponding times throughout the year No, annual flows are a random variable Yes, flows occur at a constant rate (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 (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 The middle portion of the data are found to have an annual flow between a lower value of and a higher value of The total spread of annual flows goes from a lower value of to a higher value of 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 10 8 cubic meters) 3 83 3 81 4 01 4 84 5 81 5 50 4 31 5 81 4 31 4 17 Although smaller, is the new river more reliable Use the coefficient of variation to make an estimate (Round your answers to two decimal place ) original river's coefficient of variation smaller river's coefficient of variation What do you conclude The original river is more consistent Neither river is more consistent The smaller river is more consistent (g) Based on the data, would it be safe to allocate at least 26 units of the orginal river water each year for agricultural and domestic use Why or why not Yes, Q1 is greater than 26 which means over three quarters of the river flows are at or above 26 No, Q3 is less than 26 which means more than three quarters of the river flows are below 26 No, since 26 is an upper outlier it will be very rare to have a flow at or above 26 Yes, since 26 is an lower outlier it will be very rare to have a flow below 26 No, the median is less than 26 which means more than half the river flows are below 26

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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

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	31.8	23.1	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 average out to the same value across each year.No, annual flows change at a steady rate from year to year. Yes, flows occur at the same rate at corresponding times throughout the year.No, annual flows are a random variable.Yes, flows occur at a constant rate. (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

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

The middle portion of the data are found to have an annual flow between a lower value of and a higher value of . The total spread of annual flows goes from a lower value of to a higher value of . 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

4.17

Although smaller, is the new river more reliable? Use the coefficient of variation to make an estimate. (Round your answers to two decimal place.)

original river's coefficient of variation	%
smaller river's coefficient of variation	%

What do you conclude? The original river is more consistent.Neither river is more consistent. The smaller river is more consistent. (g) Based on the data, would it be safe to allocate at least 26 units of the orginal river water each year for agricultural and domestic use? Why or why not? Yes, Q1 is greater than 26 which means over three quarters of the river flows are at or above 26.No, Q3 is less than 26 which means more than three quarters of the river flows are below 26. No, since 26 is an upper outlier it will be very rare to have a flow at or above 26.Yes, since 26 is an lower outlier it will be very rare to have a flow below 26.No, the median is less than 26 which means more than half the river flows are below 26.