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	31.3	23.6	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.

Yes, flows occur at a constant rate.    

 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.

(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	27.60
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?

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

4.37

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 27 units of the orginal river water each year for agricultural and domestic use? Why or why not? 

No, since 27 is an upper outlier it will be very rare to have a flow at or above 27.

No, Q3 is less than 27 which means more than three quarters of the river flows are below 27.     

Yes, Q1 is greater than 27 which means over three quarters of the river flows are at or above 27.

No, the median is less than 27 which means more than half the river flows are below 27.

Yes, since 27 is an lower outlier it will be very rare to have a flow below 27.