In a formula to calculate a Celsius wind chill, V would be the wind speed in kilometers per hour, and T would be the temperature in degrees Celsius.
1. Using the formula compute the Fahrenheit wind chill for a wind speed of 5 mph and a temperature of 10 °F.
2. If the wind chill reading were –20 °F and the wind speed were 10 mph, determine the temperature in degrees Fahrenheit.
20 = (0.3 x 10^{0.5 }+ 0.474  0.02 x 10)(T  91.4) + 91.4
111.4 = (0.3 x 10^{0.5 }+ 0.474  0.02 x 10)(T  91.4)
111.4 = 474.75(T  91.4)
111.4 / 474.75 = (T  91.4)
0.2346 = (T  91.4)
0.2346 +91.4 = T
91.2 = T
3. Explain how the formula for Fahrenheit wind chill could be changed to create a formula for Celsius wind chill. Use your explanation to create your own formula for Celsius wind chill.
Replace the V in the formula with the conversion formula for converting miles per hour to kilometers per mile, and replace the T with the conversion formula for converting Fahrenheit to Celsius.
Twc = (0.3 x (1.609V)^{0.5 }+ 0.474  0.02 x 1.609V)((T32)x1.8) 91.4) + 91.4
= (0.38V^{0.5 }+ 0.474  0.032V)((T  32)x1.8  91.4) + 91.4
According to the source above, a formula for Celsius wind chill is:
T(wc) = 0.045(5.27V^{0.5} + 10.45  0.28V) (T  33) + 33
Remember, V is the wind speed in kilometers per hour, and T the temperature in degrees Celsius.
4. Compare the results of using the formula you created to the results from the given formula for determining Celsius wind chill. What might cause any differences.
Using 60 °F with a wind speed of 5 mph, the formula we derived gives a wind chill of 3.14 °C.
Using the given formula and the equivalent measures of 15.5°C and 8.045 kph gives a wind chill of 14.79 °C.
The difference between the two values can be attributed to the rounding of many values of the constants used in our creation of the formula. If other values are used, the formulas lead to values whose difference will be larger or smaller. If we were to carry as many decimal places as our calculator or computer would allow, there would still be a difference, though it would be smaller.
Rainfall
3. Determine the average of the extreme temperatures for each site.
State 
Station 
Extreme High Temperature in °F 
Extreme Low Temperature in °F 
Average Extreme Temperature in °F 
Alabama 
Mobile 
104 
3 
53.5 
Alaska 
Anchorage 
85 
34 
25.5 
Alaska 
Barrow 
79 
56 
11.5 
Arizona 
Phoenix 
122

17 
69.5 
Arkansas 
Little Rock 
112 
5 
53.5 
California 
Los Angeles 
112 
28 
70 
California 
San Diego 
111 
29 
70 
California 
San Francisco 
106 
20 
63 
Colorado 
Denver 
104 
30 
37 
Connecticut 
Hartford 
102 
26 
37 
Delaware 
Wilmington 
102 
14 
44 
District of Columbia 
Washington National 
104 
5 
49 
Florida 
Jacksonville 
105 
7 
56 
Florida 
Miami 
98 
30 
59 
Georgia 
Leant 
105 
8 
48.5 
Georgia 
Savannah 
106 
3 
54 
Hawaii 
Honolulu 
94 
53 
73.5 
Idaho 
Boise 
111 
25 
43 
Illinois 
Chicago 
104 
27 
38.5 
Illinois 
Moline 
106 
27 
39.5 
Indiana 
Indianapolis 
104 
23 
40.5 
Iowa 
Des Moines 
108 
24 
42 
Kentucky 
Lexington 
103 
21 
41 
Kentucky 
Louisville 
105 
20 
42.5 
Louisiana 
New Orleans 
102 
11 
56.5 
Maine 
Caribou 
96 
41 
27.5 
Maine 
Portland 
103 
39 
32 
Maryland 
Baltimore 
105 
7 
49 
Massachusetts 
Boston 
102 
12 
45 
Michigan 
Detroit 
104 
21 
41.5 
Michigan 
Sault Ste. Marie 
98 
36 
31 
Minnesota 
Duluth 
97 
39 
29 
Minnesota 
Minneapolis 
105 
34 
35.5 
Mississippi 
Jackson 
106 
2 
54 
Missouri 
Kansas City 
109 
23 
43 
Missouri 
St. Louis 
107 
18 
44.5 
Montana 
Helena 
105 
42 
31.5 
Nebraska 
Omaha 
114 
23 
45.5 
Nebraska 
Scottsbluff 
109 
42 
33.5 
Nevada 
Reno 
105 
16 
44.5 
New Jersey 
Atlantic City 
106 
11 
47.5 
New Mexico 
Albuquerque 
105 
17 
44 
New York 
Albany 
100 
28 
36 
New York 
Buffalo 
99 
20 
39.5 
New York 
New YorkLa Guardia 
107 
3 
52 
North Carolina 
Asheville 
100 
16 
41 
North Carolina 
Raleigh 
105 
9 
48 
North Dakota 
Bismarck 
109 
44 
32.5 
Ohio 
Cleveland 
104 
19 
42.5 
Ohio 
Columbus 
102 
19 
41.5 
Oregon 
Portland 
107 
3 
52 
Pennsylvania 
Philadelphia 
104 
7 
48.5 
Pennsylvania 
Pittsburgh 
103 
18 
42.5 
Rhode Island 
Providence 
104 
13 
45.5 
South Carolina 
Charleston 
104 
6 
55 
South Dakota 
Huron 
112 
39 
36.5 
South Dakota 
Rapid City 
110 
30 
40 
Tennessee 
Memphis 
108 
13 
47.5 
Tennessee 
Nashville 
107 
17 
45 
Texas 
Galveston 
101 
8 
54.5 
Texas 
Houston 
107 
7 
57 
Utah 
Salt Lake City 
107 
30 
38.5 
Vermont 
Burlington 
101 
30 
35.5 
Virginia 
Norfolk 
104 
3 
51 
Virginia 
Richmond 
105 
12 
46.5 
Washington 
SeattleTacoma 
99 
0 
49.5 
Washington 
Spokane 
103 
25 
41.5 
Wisconsin 
Milwaukee 
103 
26 
38.5 
Wyoming 
Lander 
101 
37 
32 
The following is a scatter plot of the average extreme temperatures and the normal precipitation for each site.
3. Describe the relationship between the average extreme temperature and the normal precipitation indicated in the scatter plot.
There is very little association apparent from the graph.
4. The lower right hand corner of this plot shows a cluster of five sites. Using both the table and graph, identify these five sites and determine if there is any relationship among them.
The five cities are San Diego, San Francisco, Los Angeles, Phoenix, and Honolulu. These five cities are among the most south and/or west of all the cities.
5. What observations can you make about the relationship between the temperature and the amount of rainfall in these five cities?
They have a high average temperature and low precipitation.
The following table is from Greener Pastures Relocation Guide, 1984.
City 
Mean inches of Rainfall 
Percent Sunshine 
Los Angeles, CA 
14 
73 
Salt Lake City, UT 
15 
70 
Phoenix, AZ 
7 
86 
Las Vegas, NV 
9 
84 
San Francisco, CA 
20 
67 
Denver, CO 
16 
70 
Wichita, KS 
31 
65 
Oklahoma City, OK 
31 
67 
Albuquerque, NM 
8 
77 
Houston, TX 
48 
57 
Little Rock, AR 
49 
63 
New Orleans, LA 
57 
59 
Nashville, TN 
46 
57 
Jackson, MS 
49 
60 
Mobile, AL 
60 
67 
Charlotte, SC 
66 
43 
Raleigh, NC 
60 
43 
Miami, FL 
66 
60 
St. Louis, MO 
58 
36 
Louisville, KY 
57 
43 
Norfolk, VA 
63 
45 
6. Which city has the maximum percentage of sunshine?
Phoenix, Arizona has the maximum percentage of sunshine.
7. Which three cities have the least amount of rainfall?
Phoenix, Arizona, Albuquerque, New Mexico, and Las Vegas, Nevada have the least amount of normal annual rainfall.
8. Create a scatter plot with the rainfall on the horizontal axis and the percent of sunshine on the vertical axis.
9. Describe the graph in your own words.
The graph looks like it is decreasing and somewhat linear.
10. You can notice a cluster of points in the lower right of the graph. Explain what you know about these cities simply by their locations on the graph.
These five cities have a low percentage of possible sunshine and high annual rainfall,
11. Draw a line on the graph that represents the relationship among the data.
12. Determine the slope of your line, and explain what it tells you about the relationship between the data.
The slope of the line is approximately 0.5. The slope tell us that for every one inch increase in rainfall, the percentage of possible sunshine will decrease onehalf of a percentage point.
13. Describe the x and yintercepts in words.
The yintercept is the predicted percentage of possible sunshine when the rainfall is zero. The xintercept is the predicted inches of rainfall when the percent of possible sunshine is zero.
14. How can you tell how well this lines fits the data?
Younger and less experienced students will probably identify things like the points lying near the line and the line appearing to pass through the middle of the data.
More experienced students will probably use the least squares regression line and should refer to the sum of the squared residuals and the correlation coefficient. The correlation coefficient is 0.8078.