Test Bank for Medical-Surgical Nursing Critical Thinking in Client Care 4 Edition WITH QUE, Exams of Nursing

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WARM-UP

Each number below represents the age of a U.S. president on his first inauguration.

A) Make a stem-and-leaf plot of these ages.

B) Make a histogram of the ages of U.S. presidents on their first

inauguration using 6 classes. Make sure each class is equal in size.

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C) What was the mean age of the presidents on their first inauguration?

D) Which age(s) occur most frequently?

E) What is the median age?

F) Are there any outliers to the data?

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15.1 The Frequency Distribution

1. Frequency: how many times something occurs 2. Frequency Distribution: A set of data listed with their frequencies (usually listed with categories or class intervals) 3. Relative Frequency Distribution:

A set of data listed with their percentages (usually listed with categories or class intervals)

4. Box-and-whisker Plot: A diagram that graphically displays the median, quartiles, extreme values, and outliers in a

set of data.Whiskers extend to the extreme values of the data, unless there is an outlier When there is an outlier, then

it is the extreme value.

5. Outliers: Extreme values that are more than 1.5 of the interquartile range beyond the upper or lower quartiles.

If outliers exist, each whisker is extended to the last value of the data that is not an outlier.

6. Use the following box plot of student test scores on last year’s advanced algebra mid-year exam.

a. What is the median score?

b. What is the interquartile range?

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c. What percent of the students scored between 62 and 91?

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d. What is the interval of scores of students who ranked below the lower quartile?

7. Class intervals: Is the range of a class. In a frequency table, all class intervals should all be equal. To identify good

class intervals, find the range of the data by taking the maximum value and subtracting the minimum value. Then

divide the range into equal parts. Usually use 8 to 10 classes to give a good presentation of the data.

Ex: A television network has asked 25 viewers to evaluate a new police drama. The possible evaluations are (E)xcellent,

(A)bove average, a(V)erage, (B)elow average, (P)oor. After the show, the 25 evaluations were as follows:

A, V, V, B, P, E, A, E, V, V, A, E, P, B, V, V, A, A, A, E, B, V, A, B, V.

Construct a frequency table and a relative frequency table for this list of evaluations.

8. Bar Graph: A graphic form of data that uses bars that have space between them, where the height gives

the frequency of that category or class

Ex: Draw a bar graph of the frequency distribution of TV viewers’ responses from #5.

Ex: The bar graph shows the number of Atlantic hurricanes over a period of years. Use it to answer the

following questions.

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were the hurricanes counted?

d. In what percentage of the years were there more than ten hurricanes?

a. What was the

smallest number of

hurricanes in a year

during this period?

b. What number of

hurricanes per year

occurred most

frequency?

c. How many years

9. Back-to-back Bar Graph:

Plot on a two-quadrant coordinate system with the horizontal scale repeated in each direction from the central axis.

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Ex: Use the side by side bar graph to answer the questions.

Another view of the same data.

a. What percent of

Americans had their

associate’s degree

in 1990? 2006?

b. What percent of

Americans at least had

a high school diploma

in 1990? 2006?

c. Are a greater

proportion of

Americans dropping

out of college before

earning a degree?

10. Histogram: A type of bar graph in which the width of each bar

represents a class interval and the height of the bar represents

the frequency in that interval

1. Used to graph a frequency distribution of continuous

variable quantity

2. No spaces between bars of classes, usually have less than

ten intervals

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Ex: The New York Clinic has the following data regarding the weight lost by

its clients over the past six months. Draw a

histogram for the relative frequency distribution for this data.

Pounds Lost Frequency

0-10 14

10 + to 20 23

20 + to 30 17

30 + to 40 8

40 + to 50 3

11. Class Limit: Is the upper and lower values in a class interval. 12. Class Mark: Is the midpoint of the classes. 13. The heights (in inches) of 43 girls trying out for basketball at Forest View High School have been tallied in the

chart below.

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Class Limits Tally Frequency

58-62 ||

62-66 |||| ||

66-70 |||| |||| |||| |

70-74 |||| |||| ||

74-78 ||||

a. Determine if the class intervals of 4 are appropriate for the data.

b. Draw a histogram of the data.

14. Stem-and-leaf Plot: A display of numerical data for which each value is separated into two numbers, a stem and

a leaf. Leaves are only 1 unit long.

Ex: Make a stem-and-leaf plot to compare Babe Ruth’s and Hank Aaron’s Home Run records.

Ruth: 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22

Aaron: 44, 30, 39, 40, 34, 45, 44, 32, 44, 39, 44, 38, 47, 34, 40

15. Median: The middle value of a data set. If you have an even number of data items, then you have to find the

average of the two data items that make up the middle. Extreme values have very little influence on the median.

16. Range: The difference of the greatest and least values in a set of data. 17. Quartile: One of four groupings of a set of data determined by the median of the set and the medians of the

sets determined by the median.

18. Interquartile Range: The difference between the third quartile point and the first quartile point.

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19. The National Football League is separated into two parts-the American Football Conference (AFC) and the National

Football Conference (NFC). Here are separate box plots of the capacities of the football stadiums used by the AFC

and NFC.

a. What is the median capacity in each conference?

b. What is the size of the largest stadium in each conference?

c. About what percent of the stadiums in the AFC hold fewer than 60,000 people?

d. On the whole, which conference has larger stadiums?

20. Below is a stem plot of the amount of money spent by 25 shoppers at a grocery store. The stem is in $10 units.

0 3 8

1 0 1 7 8 9

2 0 0 3 6 8

3 1 3 4 7

4 2 5 5

5 0

6 5

7 2 6

8

9 7

10

11 3

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i= 1

( X -

Mean

1 n

i = 1

( X - X )

n

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a. Find the

median.

b. Find the

lower quartile.

c. Find the upper quartile.

d. Determine if there are any outliers.

e. Construct a box and whiskers plot.

21. Steps in the Calculator

Homework: Bar Graphs, Histograms, and Box and Whisker Plots Worksheet

Measures of Central Tendency:

Range: The difference of the greatest and least values and it measures variability.

Deviation:

Variance:

Standard (Mean) Deviation:

Population Standard Deviation versus Sample Standard Deviation

Population: Divide by ‘n’ is used when the sample is the population

Devi

mea 2

n

X )

Sample: Divide by ‘n - 1’ is used for a sample because it gives a better

estimate of the population mean

“n” =

MATH 5 34 FINAL EXAM REVISION GUIDE

i n - 1

Sx =

i n

Square of deviation

from mean

ation from

Value

x =

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4. Find the mean and standard deviation for the following

data: {3,5,6,7,9,11,22}. Use the table on the right.

USING CALC: Stat > Calc 1: 1-Var Stats

Symbol for mean: Sx = sample standard deviation calculated using (n-1)

σx = population standard deviation calculated using “n”

Value Mean Deviation from mean Square of Deviation from Mean

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AFM Unit 8 Day 3 HW Worksheet NAME

Make a box-and-whisker plot of the data. Find the five main values needed to label your diagram.

1. 29, 34, 35, 36, 28, 32, 31, 24, 24, 27, 34

TV Time (minutes)

0 15 60 110 225

2. What percent of the sophomores watch TV for at least 15 minutes per night?
3. What is the 3

rd quartile for the TV time data?

Find the mean and standard deviation of each data set.

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1st Period 3 04 8 5 35 9 6 5 2 06 5 5 2 07 5 2 18 9 0 0 010 3rd Period 2 9 8 0 5 8 8 8 9 0 2 4 5 5 5 6 0 3 5 8

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1.{200, 476, 721, 579, 152, 158} 2.{369, 398, 381, 392, 406, 413, 376, 454, 420, 385, 402, 446}

3.Given the quiz grades in Theresa Chair’s two sections of Geometry, answer the following questions. a. Find the mean for 1 st period. b. Find the standard deviation for 1 st period. Will you use population or sample? Why? c. Find the mean for 3 rd period. d. Find the standard deviation for all Ms. Chair’s Geometry students. Will you use population or sample? Why? Determine whether the data in each table appear to be left-skewed, right-skewed, or normally distributed, or bimodal 1.U.S. Population 5. Record Low Temperatures in the 50 States 6. GPAs of Jr at Apex

7.Ti of High School Principals 9.

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Age Percent Temperature ( ) Number of States 0-19 28. 4 20-39 29. 12 40-59 25. 19 60-79 13. GPA Frequency 0.0-0.4 4 0.5-0.9 4 1.0-1.4 2 1.5-1.9 32 2.0-2.4 96 Minutes Frequency

0-25 27

26-50 46 51-75 89

Age in Years Number 31-35 3 36-40 8 41-45 15 46-50 32 Shoe Size 4 5 6 7 8 9 10 No. Of students me Spent in a Muse 1 um 2 4 8

5 Av e 1 rage 2 Age

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33

Sampling Techniques and Misuses

1. Statistics:

The science of collecting, organizing, summarizing, and analyzing information to draw conclusions or

answer questions. In addition, statistics is about providing a measure of confidence in any conclusions.

2. Population:

The entire group of individuals that we want information about

3. Sample:

A part of the population that we actually examine in order to gather information. The sample is used to

make generalizations of the population.

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4. Qualitative Data:

Data that measures the classification of individuals based on some attribute or characteristic

5. Quantitative Data:

Data that provides numerical measures of individuals.

Ex: Determine whether the following variables are qualitative or quantitative.

a. Gender

b. Temperature

c. Number of days during the past week that a college student

aged 21 years or older has had at least one drink.

d. Zip code

6. Discrete Variable:

A quantitative variable that has either a finite number of possible values or a countable number of values

7. Continuous Variable:

A quantitative variable that has an infinite number of possible values that are not countable.

Ex: Determine whether the following quantitative variables are discrete or continuous.

a. The number of heads obtained after flipping a coin five times.

b. The number of cars that arrive at a McDonald’s drive-

through between 12:00 P.M. and 1:00 P. M.

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c. The distance a 2007 Toyota Prius can travel in city driving conditions with a full tank of gas.

8. How do we gather data? - Surveys - Observational Studies - Experimental Studies - Simulations 9. Observational Study:

Investigators observe subjects and measure variables of interest without assigning treatments to the

subjects. The treatment that each subject receives is determined beyond the control of the investigator.

*Do not allow a researcher to claim causation, only association.

10. Experimental Study:

Investigators apply treatments to experimental units (people, animals, plots of land, etc.) and then proceed

to observe the effect of the treatments on the experimental units.

11. Simulations:

The use of a mathematical model to recreate a situation, often repeatedly, so that the likelihood of various

outcomes can be more accurately estimated.

Ex: Identify each as an observational study, experimental study, survey or simulation.

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a. The muscles of men aged 40 - 50 were 40% to 50% stronger after they participated in a 10 week,

high-intensity, resistance training program twice a week.

b. On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he

gets exactly two "at bats" in every game. Estimate the likelihood that the player will hit 2 home

runs in a single game.

c. Forty volunteers suffering from insomnia were divided into two groups. The first group was

assigned to a special no-desserts diet while the other continued desserts as usual. Half of the people

in these groups were randomly assigned to an exercise program, while the others did not exercise.

Those who ate no desserts and engaged in exercise showed the most improvement.

d. In 2001, a report in the Journal of the American Cancer Institute indicated that women who work

nights have a 60% greater risk of developing breast cancer. Researchers based these findings on

the work histories of 763 women with breast cancer and 741 women without the disease.

e. Scientists at a major pharmaceutical firm investigated the effectiveness of an herbal compound to

treat the common cold. They exposed each subject to a cold virus, and then gave him or her either

the herbal compound or a sugar solution known to have no effect. Several days later, they

assessed the patient’s condition, using a cold severity scale of 0 to 5.

12. Sampling Design: refers to the method used to choose the sample from the population 13. Sampling Frame: a list of every individual in the population 14. Simple Random: - consist of n individuals from the population chosen in such a way that every individual has an equal

chance of being selected

Suppose we were to take a Simple Random Survey (SRS) of 100 Apex students – Put each students’ name

in a hat. Then randomly select 100 names from the hat. Each student has the same chance to be selected!

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Not only does each student have the same chance to be selected – but every possible group of 100

students has the same chance to be selected! Therefore, it has to be possible for all 100 students to

be seniors in order for it to be an SRS!

• Advantages: Unbiased
• Disadvantages: Large variance, may not be representative. It must have a sampling frame (list

of population)

15. Stratified random sample: - population is divided into homogeneous groups called strata

Homogeneous groups are groups that are alike based upon some characteristic of the group

members.

• SRS’s are pulled from each strata

Suppose we were to take a stratified random sample of 100 APEX students. Since students are already

divided by grade level, grade level can be our strata. Then randomly select 50 seniors and randomly

select 50 juniors.

• Advantages: More precise unbiased estimator than SRS, Less variability, Cost reduced if strata

already exists

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• Disadvantages: Difficult to do if you must divide stratum, Formulas for SD & confidence

intervals are more complicated, Need sampling frame

16. Cluster Sample: - based upon location - randomly pick a location & sample all there

Suppose we want to do a cluster sample of APEX students. One way to do this would be to randomly

select 10 classrooms during 2

nd period. Sample all students in those rooms!

• Advantages: Unbiased, Cost is reduced, Sampling frame may not be available (not needed)
• Disadvantages: Clusters may not be representative of population, Formulas are complicated 17. Convenience Sample:
• Ask people who are easy to ask
• Produces bias results

An example would be stopping friendly-looking people in the mall to survey. Another example is the

surveys left on tables at restaurants - a convenient method!

The data obtained by a convenience sample will be biased – however this method is often used for

surveys & results reported in newspapers and magazines!

Ex: Identify the sampling design.

a. The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all

colleges into groups of similar types (small public, small private, etc.) Then they randomly

selected 3 colleges from each group.

b. A county commissioner wants to survey people in her district to determine their opinions on a

particular law up for adoption. She decides to randomly select blocks in her district and then survey

all who live on those blocks.

18. Bias: - A systematic error in measuring the estimate

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• favors certain outcomes

Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent,

or to the sampling method!

Sampling Design Worksheet Name:

I. Classify the variable as qualitative or quantitative.

1. Number of siblings
2. Grams of carbohydrates in a doughnut
3. Number on a football player’s jersey
4. Number of unpopped kernels in a bag of ACT microwave popcorn
5. Assessed value of a house
6. Phone number
7. Student ID number

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II. Determine whether the quantitative variable is discrete or continuous.

8. Runs scored in a season by Albert Pujols
9. Volume of water lost each day through a leaky faucet.
10. Length (in minutes) of a country song
11. Number of sequoia trees in a randomly selected acre of Yosemite National Park
12. Temperature on a randomly selected day in Memphis, Tennessee
13. Internet connection speed in kilobytes per second
14. Points scored in an NCAA basketball game
15. Air pressure in pounds per square inch in an automobile tire

III.Determine whether the study depicts an observation study, experimental study, simulation or

a survey.

16. Researchers wanted to know if there is a link between proximity to high-tension wires and the rate of

leukemia in children. To conduct the study, researchers compared the incidence rate of leukemia for

children who lived within ½ mile of high-tension wires to the incidence rate of leukemia for children who

did not live within ½ mile of high-tension wires.

17. Rats with cancer are divided into two groups. One group receives 5 milligrams (mg) of a medication that is

thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the cancer is measured.

18. Rolling a pair of dice to determine the chance of getting a five or a two.

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19. Seventh-grade students are randomly divided into two groups. One group is taught math using traditional

techniques; the other is taught math using a reform method. After 1 year, each group is given an

achievement test to compare proficiency.

20. Using a coin to estimate the percent of families that have one boy when there is three children.
21. A poll is conducted in which 500 people are asked whom they plan to vote for in the upcoming election.
22. A survey is conducted asking 400 people, “Do you prefer Coke or Pepsi?”
23. While shopping, 200 people are asked to perform a taste test in which they drink form two

randomly placed, unmarked cups. They are then asked which drink they prefer.

24. Conservation agents netted 250 large-mouth bass in a lake and determined how many were

carrying parasites.

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IV. Determine the sample design.

25. To determine customer opinion of its boarding policy, Southwest Airlines randomly selects 60

flights during a certain week and surveys all passengers on the flights.

26. In an effort to identify if an advertising campaign has been effective, a marketing firm conducts

a nationwide poll by randomly selecting individuals from a list of known users of the product.

27. A farmer divides his orchard into 50 subsections, randomly selects 4, and samples all the trees within the 4

subsections to approximate the yield of his orchard.

28. To determine his DSL Internet connection speed, Shawn divides up the day into four parts: morning

midday, evening, and late night. He then measures his Internet connection speed at 5 randomly

selected times during each part of the day.

29. A large medical professional organization with membership consisting of doctors, nurses, and other medical

employees wanted to know how its members felt about HMOs (health maintenance organizations). Name

the type of sampling plan they used in each of the following scenarios:

a. They randomly selected 500 members from each of the lists of all doctors, all nurses, and all

other employees and surveyed those 1500 members.

b. They randomly selected ten cities from all cities in which its members lived, and then surveyed

all members is those cities.

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30. A political scientist surveys 400 voters randomly selected from the list of all registered voters in a

community. The purpose is to estimate the proportion of registered voters who will vote in an

upcoming election.

15.4 The Normal Distribution

1. Normal Distribution: A frequency distribution that often occurs when there is a large number of values in a

set. The distribution of data along a bell-shaped, symmetric curve that reaches its maximum height at the mean.

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