1 Doctors: The following tab
1 Doctors:
The following table is a list of the number of MD’s per 100,000 people in 2002 as reported as an indicator of the availability of health care in the 50 states and the District of Columbia. The values are ranked from in descending order.
D.C. |
683 |
MAINE |
250 |
MONTANA |
215 |
MASSACHUSETTS |
427 |
TENNESSEE |
250 |
KANSAS |
210 |
NEWY ORK |
385 |
WASHINGTON |
250 |
GEORGIA |
208 |
MARY LAND |
378 |
OHIO |
248 |
INDIANA |
207 |
CONNECTICUT |
360 |
DELAWARE |
242 |
TEXAS |
204 |
V ERMONT |
346 |
OREGON |
242 |
ALABAMA |
202 |
RHODEISLAND |
341 |
NORTHCAROLINA |
241 |
SOUTHDAKOTA |
201 |
NEWJERSEY |
305 |
FLORIDA |
237 |
UTAH |
200 |
PENNSY LV ANIA |
291 |
COLORADO |
236 |
ARIZONA |
196 |
HAWAII |
280 |
MISSOURI |
233 |
ALASKA |
194 |
ILLINOIS |
265 |
MICHIGAN |
230 |
ARKANSAS |
194 |
MINNESOTA |
263 |
NEBRASKA |
230 |
IOWA |
178 |
LOUISIANA |
258 |
NORTHDAKOTA |
228 |
WY OMING |
176 |
WISCONSIN |
256 |
NEWMEXICO |
222 |
NEV ADA |
174 |
V IRGINIA |
253 |
WESTV IRGINIA |
221 |
MISSISSIPI |
171 |
CALIFORNIA |
252 |
KENTUCKY |
219 |
OKLAHOMA |
163 |
NEWHAMPSHIRE |
251 |
SOUTHCAROLINA |
219 |
IDAHO |
161 |
1. Who are the ”individuals” or ”elements” described in this data set?
The number of doctors
2. What is the variable observed or measured to each ”individual” or ”element”?
How many doctors are in each state
3. Why was this study done?\
To see the availability of healthcare providers
4. When was the study done? In 2002
5. Fill in the Table of Frequencies and Percents within each of the intervals.
Interval |
Frequency |
% withn interval |
6. Draw the Histogram of Number of Doctors per 100,000 in the space provided or copy from Minitab.
7. How would you describe the shape of the distribution of the Number ofDoctors per 100,000 people?
8. What percent of the states have between 200 and 300 doctors for every100,000 people.
9. Do you think that the majority of states have More or Less than 300 doctors per 100,000 people?
10. The mean x of the 51 observations is 251.9. Do you expect the median to be Higher or Lower than the mean? Why?
11. The range is just the difference between the maximum and the minimum value. What is the range of the data?
12. Find the Five Number Summary?
13. By using the 1.5IQR Rule, List the seven observations(the states or D.C.) that may be classified as outliers.
14. Draw the Box-Plot of the Data either by hand or via software. Rememberto represent the outliers with either an X or an O.
15. Briefly discuss the results above by interpreting what you believe is revealed when discussing the availabiliy of heath care in the 50 states and Washington D.C.
2 Bar Charts: Spam Emails
Here is a compilation of the most common types of spam emails.
Type of spam |
Percent |
Adult |
19 |
Financial |
20 |
Health |
7 |
Internet |
7 |
Leisure |
6 |
Products |
25 |
Scams |
9 |
1. Do the Percentages add to 100%? What Percentage will be left for a category of Other?
2. Create a Bar chart of the variable Type of Spam in the space provided either by hand or via Minitab.
3. Can we ever discuss shape, center, or spread with a Categorical variable?
Yes or No.
3 Summary Statistics
Here are the lengths of right-hand span widths (cm) of a sample of 7 students.
8.9 23 18 14 8 9.5 12
1. Calculate the mean ¯x and the Median M
2. Calculate the Standard Deviation s
3. Calculate the Five Number Summary
4. Why do you believe the mean is much larger than the median?
5. What would happen to the values of the summary statistics if we foundout that right-hand span of a 23 cm was a typo and should have instead been a 13 cm instead? Just say either increase, decrease, or stay the same for the each value below.
x¯ |
s |
min |
Q_{1} |
M |
Q_{3} |
Max |
6. What would happen to the summary statistics if each data value wasconverted to inches? There are 2.54 cm to an inch.
4 Normal Distributions
4.1 Using the 68-95-99.7 Rule
Scores on a University exam are normally distributed with a mean µ of 68 and a standard deviation σ of 9. Use the 68-95-99.7 Rule to answer the following questions.
1. Draw the Density Curve and label ±3σ away from the mean.
2. What proportion of students score between a 59 to 77?
3. What proportion of students score between a 50 to 86?
4. What proportion of students score above a 86?5. What proportion of students score below a 41?
6. What proportion of students score above a 59?
7. What must a student score on the exam to be in the bottom 2.5% of scoreson the exam?
4.2 Using Table A (Standard Normal Distribution) to find Percentiles
1. Find z < 1.96
2. Find z < −2.46
3. Find z > 1.50
4. Find z > −1.00
5. Find −1.25 < z < 1.75
4.3 Finding Proportions for a Normal Distribution with mean µ and standard deviation σ (AKA Finding zscores to use Table A)
It has been shown that lengths of pregnancies follow a Normal Distribution with mean µ of 266 days and standard deviation σ of 16 days. Use this information to answer the following questions.
1. Draw the Density Curve for Lengths of Pregnancies.
2. What proportion of pregnancies last less than 275 days?
3. What proportion of pregnancies last more than 275 days?
4. What proportion of pregnancies last between 245 days and 280 days?
5. What proportion of pregnancies last less than 290 days?
6. What proportion of pregnancies last more than 255 days?