Quiz 1

Question 1

The term statistics can have two meanings

Answer 1

Statistics is the science of collecting, organizing, and interpreting data and statistics are the data (numbers or other pieces of information) that describe or summarize something

Question 2

Each year, a group surveys 50,000 households to study internet usage
- In one area of the study, the group is interested in finding out how many hours a day the household spends streaming video from the internet
- Describe the five basic steps in a statistical study with an example of their application below

Answer 2

1. State the goal of your study. In this case, it is to discover how many hours per day a household spends streaming internet video.
2. Choose a representative sample from the population. In this case, it would be choosing a sample of 50,000 households.
3. Collect raw data from the sample and summarize these data by finding sample statistics of interest.in this case, it would be asking the households how many hours they spend streaming internet video and turning this data into an average.
4. Use the sample statistics to infer the population parameters. In this case, based on the data gathered, the group estimates the average time per day that a household spends streaming internet
   video.
5. Draw conclusions to determine what you learned and whether you achieved your goal. In this case, we discovered the average time per day that a household spends streaming internet video.

Question 3

In a test of the effectiveness of garlic for lowering cholesterol, 57 adult women were treated with garlic in a processed tablet form.
- Cholesterol levels were measured before and after the treatment.
- The changes in their levels of LDL cholesterol (in mg/dL) have an average (mean) of 4.9.
- Identify the sample, the population, the sample statistic, and the population parameter in this study

Answer 3

All adult women

Question 4

Use the given statistics and margin of error to identify the range of valves (confidence interval) likely to contain the true value of the population parameter.
- In a poll of 1,586 randomly selected adults in a certain country, 72% said that global warming is already harming people around the world.
- The margin of error is 4 percentage points

Answer 4

The range of values likely to contain the population parameter is from 68% to 76%
- Whole numbers only, use ascending order (low to high)
- From = sample statistic - margin of error
- To = sample statistic + margin of error

Question 5

In a poll, surveyed men were asked if they agreed with this statement: “abortion is a private matter that should be left to women to decide without government intervention.”
- Among the men who were interviewed by women, 71% agreed with the statement.
- Among the men who were interviewed by men, 63% agreed with the statement.
- Assuming that the discrepancy is significant, how might that discrepancy be explained?

Answer 5

Men may think that agreeing is the response the female interviewers favor

Question 6

What is a census, what is a sample, and what is the difference between them?

Answer 6

A census is the collection of data from every member of the population, but a sample is the collection of data from only a part of the population

Question 7

What is a biased sample, and what is a major problem with it?

Answer 7

A biased sample is a sample where the members of the sample differ in some specific way from the members of the general population.
- The major problem with a biased sample is that the results obtained from a biased sample are likely to be misleading.

Question 8

In a Gallup poll of 1,038 randomly selected American teachers, 89% said that they feel vulnerable to identify theft.
- Identify the sample, population, and sampling method.
- Then comment on whether you think it is likely that the sample is representative of the population.

Answer 8

1. Sample - The 1,038 randomly selected American teachers.
2. Population - All American teachers.
3. Sampling method - Random.
4. Comment - The sample is fairly large and random. Assuming it was obtained by a reputable firm, the sample is likely to be representative of the population.

Question 9

Determine whether there is a potential for bias and explain your answer.
- A researcher for the department of transportation surveys 3200 randomly selected adults by asking them if they possess a valid driver’s license.

Answer 9

There do not appear to be any sources of bias, because the researcher has nothing to gain by distorting the results and the department of transportation is likely to use sound sampling methods

Question 10

On days of governor elections, the news media organize an exit poll in which specific polling stations are randomly selected and all voters are surveyed as they leave the premises.

Answer 10

1. What type of sampling is used?
   - Cluster sampling
2. Is the procedure likely to yield a representative sample or a biased sample?
   - The procedure is likely to be representative because the polling stations are randomly chosen and because all people at the chosen polling stations are part of the sample.

Question 11

An engineering student measures the strength of fingers used to press the buttons on a newly designed gas station pump by testing her own family members.

Answer 11

1. What type of sampling is used?
   - Convenience sampling
2. Is the procedure likely to yield a representative sample or a biased sample?
   - The procedure is likely to be biased, because it consists of family members likely to have similar physical characteristics and exercise habits.

Question 12

A marketing expert for a particular magazine is planning a survey in which 478 people will be randomly selected from each age group: 10-19, 20-29, and so on.

Answer 12

1. What type of sampling is used?
   - Stratified sampling
2. Is the procedure likely to yield a representative sample or a biased sample?
   - The procedure is likely to be biased because people from those age groups are not evenly distributed throughout the population.

Question 13

A college dean obtains an alphabetical list of all full time students at her college and she selects every 12th name on that list and interviews those students to find the amount of student debt incurred by each of them.
- She uses the results to estimate the average (mean) amount of student debt incurred by college students in the United States.

Answer 13

1. What type of sampling is used?
   - Systematic sampling
2. Is the procedure likely to yield a representative sample or a biased sample?
   - The procedure is likely to yield a biased sample because the students she interviews are all from the same school.

Question 14

A sample of manufactured tires is obtained by using a computer to randomly generate a number between 1 and 900, inclusive, for each tire, and the tire is tested if the generated number is 900

Answer 14

1. What type of sampling is used?
   - Simple random sampling
2. Is the procedure likely to yield a representative sample or a biased sample?
   - The procedure is likely to yield a representative sample because a simple random sampling is unlikely to yield a biased sample.

Question 15

Define variable, variables of interest, explanatory variable, and response variable.
- How are the explanatory and response variables related to each other?

Answer 15

1. Define variable.
   - Any item or quantity that can vary or take on different values.
2. Define variables of interest.
   - The items or quantities that the study seeks to measure in a statistical study.
3. Define explanatory variable.
   - A variable that may explain or cause the effect.
4. Define response variable.
   - A variable that responds to changes in the explanatory variable.
5. How are the explanatory and response variables related to each other?
   - The explanatory variable may cause the response variable to change.

Question 16

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly.

I plan to use a double blind experiment to test the hypothesis that people will experience a decrease in their pulse rate if they exercise vigorously for 40 minutes every day.

Answer 16

The statement does not make sense.
- The subjects who exercise will know that they are exercising.

Question 17

Determine whether the following study is an observational study, an experiment, or a meta analysis, and explain your choice.

A study of 2,000 monthly cell phone bills, in the last year, identified the proportion of messages in all outgoing communications.

Answer 17

The study is an observational study because there was no attempt to influence the results.

Question 18

Determine whether the study is an observational study, an experiment, or a meta analysis, and explain your choice.

In a study of the XSORT gender selection method developed by the Genetics and IVF institute, 942 couples given treatment had 64 male babies and 878 female babies.

Answer 18

This study is an experiment because there was subjects were given a treatment.
- The treatment group consists of the 942 couples given the XSORT treatment.
- The control group consists of others not given any treatment.

Question 19

In a comparison of gasoline with different octane ratings, 5 subcompact cars are driven with 87 octane gasoline, while 4 limousines are driven with 91 octane gasoline.
- After being driven for 250 miles, the amount of gasoline consumed is measured for each vehicle.
- The researchers doing the gasoline consumption measurements are not aware of which vehicles receive 87 octane gasoline and which receive 91 octane gasoline.
- Identify any problems that are likely to cause confounding and explain how the problems could be avoided.

Answer 19

1. Identify any problems that are likely to cause confounding.
   - If there are differences in the amount of gasoline consumption, there is no way to know if the differences are attributable to the treatments (87 or 91 octane) or to the type of vehicle (subcompact car or limousine).
   - The groups are so small that confounding is likely to be introduced by the selection of the group subjects.
2. Explain how the problems could be avoided.
   - Differences in the gasoline consumption measurements can be correctly attributed to octane level by using 87 octane gasoline in half of the subcompact cars and half of the limousines and by using 91 octane gasoline in the other vehicles.
   - The size of the groups should be increased to eliminate the possibility of a biased sample.

Question 20

An article noted that chocolate is rich in flavonoids.
- The article reports that “regular consumption of foods rich in flavonoids may reduce the risk of coronary heart disease.”
- The study received funding from a candy company and a chocolate manufacturers association.
- Identify and explain at least one source of bias in the study described.
- Then suggest how the bias might have been avoided.

Answer 20

The researchers may have been more inclined to provide favorable results because funding was provided by a party with a definite interest.
- The bias could have been avoided if the researchers were not paid by the candy company and the chocolate manufacturers.

Question 21

A voter receives a call in which the caller claims to be conducting a national opinion research poll.
- The voter is asked if their opinion about a congressional candidate would change if they knew that the candidate once had a car crash while driving under the influence of alcohol.
- Identify and explain at least one source of bias in the study described.
- Then suggest how the bias might have been avoided.

Answer 21

The wording of the question is biased to strengthen opposition against a particular candidate.
- The question wording should be changed to be more neutral.

Question 22

The headline “Drugs shown in 98 percent of movies” accompanied a news story that described a “government study” claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals.
- Discuss whether the headline accurately represents the story.

Answer 22

The headline refers to drugs whereas the story refers to “drug use, drinking, or smoking.”
- The headline is very misleading because the term “drugs” is generally considered to consist of drugs other than cigarettes or alcohol.
- Also, all movies consist of more than just the top movie rentals.

Question 23

Much like sound bites of news stories, statistical studies are often reduced to one or two sentence stat-bytes.
- For the following stat-byte, discuss what crucial information is missing and what more you would want to know before acting on the study.

CNN reported on a Zagat survey of America’s top restaurants that found that “only nine restaurants achieved a rare 29 out of possible 30 rating and none of those restaurants are in the Big Apple.”

Answer 23

Which of the following are crucial pieces of information that you would want to know before acting on the study?
1. How the respondents were selected.
2. Who the respondents in the survey were.
3. How the quality of restaurants was measured.

Question 24

Determine whether the data described below are qualitative or quantitative and explain why.

The numbers of students in the graduating class at different high schools.

Answer 24

The data are quantitative because they consist of counts or measurements.

Question 25

Determine whether the following variable is qualitative or quantitative. The yes/no responses on a ballot initiative to the question “should the highway speed limit be increased?”

Answer 25

The variable is qualitative because yes/no responses on a ballot initiative are no numerical categories.

Question 26

Determine whether the data described below are qualitative or quantitative and explain why. The distances from home to campus (in miles) of randomly selected college students.

Answer 26

The data are quantitative because they consist of counts or measurements.

Question 27

State whether the data described below are discrete or continuous, and explain why. The numbers of words in books.

Answer 27

The data are discrete because the data can only take on specific values.

Question 28

State whether the data described below are discrete or continuous, and explain why. The exact depths of the ocean at different points around the world.

Answer 28

The data are continuous because the data can take on any value in an interval.

Question 29

For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio. The genders of people.

Answer 29

Nominal

Question 30

For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio. The sizes of coffee offered by a coffee shop (small, medium, large).

Answer 30

Ordinal

Question 31

For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio. The numbers of bedrooms in houses.

Answer 31

Ratio

Question 32

Determine whether the given statement represents a meaningful ratio, so that the ratio level of measurement applies. Explain. One rock has a temperature of 120 degrees Fahrenheit and another rock has a temperature of 60 degrees Fahrenheit, so the first rock is twice as hot as the second rock.

Answer 32

The ratio level does not apply because the measurement of temperature has an arbitrary zero point

Question 33

Determine whether the data described below are qualitative or quantitative and also identify their level of measurement. - If the data is quantitative, state whether they are continuous or discrete, and give a brief explanation. Pain ratings on a 1 to 10 scale.

Answer 33

1. The data are qualitative and are at the ordinal level of measurement because the data are not counts or measurements and can be ranked. 2. The data are qualitative.

Question 34

Determine whether the data described below are qualitative or quantitative and also identify their level of measurement. - If the data are quantitative, state whether they are continuous or discrete, and give a brief explanation. The salaries of nurses at a hospital are used to determine their pension plans.

Answer 34

1. The data are quantitative and are at the ratio level of measurement because the data are counts or measurements and have a true zero point. 2. The data are discrete because the salary can only be a whole number.

Question 35

Distinguish between accuracy and precision. - Give an example of a measurement that is precise but inaccurate and another example of a measurement that is accurate but imprecise.

Answer 35

1. Give an example of a measurement that is precise but most likely to be inaccurate. - A pet cat weighs 109.55 pounds. 2. Give an example of a measurement that is accurate but imprecise. - The high temperature for a summer day in Hawaii is 90 degree farenheit

Question 36

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. In a recent year, the value of cross border trade in counterfeit and pirated goods was $254.63 billion.

Answer 36

The statement does not make sense. - The number is too precise. - There are too many unknowns and uncertainties that prevent the value from being determined with such precision.

Question 37

An FDA agent inspects shipment weights of cereal boxes to identify the following: (1) incorrect entries that were intentionally made to increase the shipment weights and (2) incorrectly recorded weights of shipments. - Discuss whether each problem involves random or systematic errors.

Answer 37

1. Do incorrect entries that were intentionally made to increase the shipment weights involve random or systematic errors? - Systematic, because the cause of the error affects all measurements in the same way. 2. Do incorrectly recorded weights of shipments involve random or systematic errors? - Random, because they represent an unpredictable event in the measurement process.

Question 38

When weighing items, a supermarket clerk mistakenly forgets to tare (calibrate) the scale, and when the weighing is completed, it is noted that the scale reads - 1.5 with nothing on it. - Is this type of error a random error or a systematic error? Explain.

Answer 38

This is systematic error, because the clerk consistently underestimates weights.

Question 39

One of the authors received a credit card bill for $3,494, but it included a charge of $1,746 that was not valid. Find the values of the absolute and relative errors.

Answer 39

- The value of the absolute error is $1746. - The value of the relative error is 100%. Relative error = absolute error divided by true value x 100% True value = the claimed value - the absolute error is Absolute error = measured value - true value

Question 40

The actual (true value) amount of change due after a gallon of milk is purchased is $12.00, but the incorrect amount of $7.00 is given instead. - Find the values of the absolute and relative errors.

Answer 40

- The absolute error is $-5. - The relative error is $-41.67%

Question 41

A new Corvette weighs 3,276 pounds. - A manufacturer’s scale that is accurate to the nearest 10 pounds gives the weight as 3282 pounds, while the Department of Transportation uses a scale that is accurate to the nearest 0.1 pound and obtains a weight of 3287.3 pounds. - Which measurement is more precise? - Which measurement is more accurate?

Answer 41

1. Which measurement is more precise? - The Department of Transportation scale is more precise. 2. Which measurement is more accurate? - The manufacturer’s scale is more accurate.

Question 42

Distinguish between absolute and relative change. - Give an example that illustrates how we calculate a relative change. Suppose your salary is $20, but then you get a raise to $21.25. - Illustrate how to calculate the relative change.

Answer 42

The relative change is $21.25 - $20 divided by $20 x 100 = 6.25%

Question 43

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. The price of a gallon of gas is quadrupled, so it increased by 400%.

Answer 43

The statement is false. - If a value is quadrupled, it increased by 300%.

Question 44

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. My bank raised its interest rate on savings accounts from 2% to 2.8%, which was a 40% increase.

Answer 44

The statement is true. - To determine how much a value increased by, the relative change should be computed. - In this case, the relative change is 40%.

Question 45

A study was conducted of pleas made by 1,030 criminals. - Among those criminals, 958 pled guilty, and 398 of them were sentenced to prison. - Among the 72 other criminals, who pled not guilty, 54 were sent to prison.

Answer 45

1. What percentage of the criminals pled guilty? - 93% 2. What percentage of the criminals were sent to prison? - 43.9% 3. Among those who pled guilty, what is the percentage who were sent to prison? - 41.5% 4. Among those who pled not guilty, what is the percentage who were sent to prison? - 75% - Find the proportion first. Proportion = criminals who pled guilty divided by total criminals. - Convert the proportion to a percentage by x 100. - Add the number of criminals who pled guilty and were sent to prison and the number of criminals who pled not guilty and were sent to prison. - Proportion is total criminals who were sent to prison divided by total criminals. - Convert the proportion to percentage by x 100. - The number of criminals who pled guilty that went to prison divided by the number of total criminals that pled guilty. - Convert to percentage x 100. - The number of prisoners who pled not guilty and were sent to prison divided by the number of criminals total who pled guilty. - Convert to percentage by x100.

Question 46

The following statement provides two values. - For the pair of values, use a percentage to express their relative change or difference. - Use the second given value as the reference value. - Also, write statement describing the result. The population for a particular region is now 317,553,426, and in 1999 it was 269,107,507.

Answer 46

1. The relative change is 18% 2. Write a statement describing the result. Select all that apply. - The population increased by the amount of the relative change from 1999 to now. - The population now is P% more than the population in 1999, where the relative change equals P%.

Question 47

Last February there were 737,861 scheduled passenger flights in a certain country, and in February of 1999 there were 637,931. Use a percentage to express the relative change. - Use the second given value as the reference value. - Also, write a statement describing the result.

Answer 47

1. The relative difference between February of 1999 and last February is 16%. 2. There is a 16% increase in the number of scheduled passenger flights from February 1999 to last February. Relative change = The new value - reference value divided by reference value x100

Question 48

The five year survival rate for caucasians for all forms of cancer increased from 38% in the 1960s to 60% now. - Express this change in two ways: 1. As an absolute difference in terms of percentage points. 2. As a relative difference in terms of percent.

Answer 48

1. The five year survival rate for Caucasians for all forms of cancer increased by 22 percentage points. 2. The five year survival rate increased by 57.9% Absolute difference = new value - reference value. Relative difference = new value - reference value divided by reference value x100

Question 49

Determine whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). - The explanation is more important than the answer. The third category in a frequency table has a cumulative frequency of 150.

Answer 49

The statement makes sense. - Even though no details are given, it is possible for the sum of the frequencies for the first three categories in a table to be 150, or any other whole number.

Question 50

A frequency table of grades has five classes.

Answer 50

Formula: Frequency is the series of numbers. Cumulative frequency is the sum of the categorical frequency and all the previous frequencies before it.

Question 51

Relative Frequency

Answer 51

Formula: Relative frequency = the frequency in the category divided by the total frequency and then x100 to convert to percentage.

Question 52

Which type of graph would work best for depicting data consisting of one value from each of the past 50 consecutive years? What is a major advantage of this type of graph?

Answer 52

A time series graph (histogram) would work best for these data. - A major advantage of this type of graph is that it allows us to see a pattern of the data over time.

Question 53

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). A quality control engineer wants to draw attention to the car parts that require repair most often, so she uses a Pareto chart to illustrate the frequencies of repairs for the various car parts.

Answer 53

Makes sense because the Pareto chart puts the bars in order of frequency and therefore will make it easy to see which repairs occur most often.

Question 54

Briefly describe how each of the following can be used to show multiple data sets: - A multiple bar graph, a multiple line chart, and a stack plot. - When is the stack plot most useful?

Answer 54

1. A multiple bar graph uses a set of bars for each data set. 2. A multiple line chart uses a different line on the same chart for each data set. 3. A stack plot is similar to a multiple bar graph or multiple line chart, except that each subsequent bar or line is added to the prior one(s) rather than shown independently. 4. A stack plot is best used with cumulative or relative frequency data, including time series data. It is most useful when the total of the data sets is important.

Question 55

Determine whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly. On a stacked bar chart, the longest bar must also have the highest value in every individual category.

Answer 55

The statement does not make sense. - The longest bar could have a very large value in one category but small values in other categories.

Question 56

Explain how a graph that shows percentage change can show descending bars (or a descending line) even when the variable of interest is increasing.

Answer 56

The vertical axis on the graph represents a percentage change such that the drop off means only the actual value of the variable rises by smaller amounts.

Question 57

Determine whether the statement below makes sense or does not make sense. Explain clearly. I drew a map on which I scaled the lengths (from east to west) or different counties (representing area) based on their numbers of family owned farms, and found that a county with twice as many farms as another ended up looking four times as large.

Answer 57

This does not make sense. - Since the map is only scaled in one direction, the size of each county is directly proportional to the number of family owned farms.

Question 58

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. There’s been only a very slight rise in our stock price over the past few months, but I wanted to make it look dramatic so I started the vertical scale from the lowest price rather than from zero.

Answer 58

The statement makes sense because reducing the range of the vertical axis to just fit the data will increase the relative size of the variation in the data.

Question 59

Weekly instruction time for a school student in one country is 21.3 hours compared to 26.3 hours in another country. - Is the difference meaningful? - How could a graph be constructed so that the difference is greatly exaggerated?

Answer 59

The difference of 5 hours is meaningful. - To exaggerate the difference, use a bar graph and start the vertical scale at 20 hours.

Question 60

The accompanying figure shows the percentage change in the Consumer Price Index (CPI) over recent years (end of year 12 month percentage change over all items) for a certain country. - Complete parts A through D below.

Answer 60

A. In what year (of the years displayed) was the change in the CPI the greatest? - 2005 B. In what year (of those displayed) was the actual CPI the highest? How do you know? - The year 2020 had the highest actual CPI because the actual highest CPI includes the change from all previous years C. Briefly explain the meaning of the red bar for 2015. Choose the correct answer below. - The CPI decreased in 2015. D. If you were to graph the actual CPI between 2006 and 2011, would the graph trend upward or downward? Explain. - The graph would trend upward because most or all of the bar heights are greater than 0.

Question 61

Children living near a smelter in Texas were found to have unusually high concentrations of lead in their bloodstreams. - Researchers studying the impact of lead poisoning measured the IQ scores of these children. - The results are shown on the accompanying histogram. - Complete parts A through E.

Answer 61

A. Estimate the frequency for each of the six categories. 40-59: 3; 60-79: 13; 80-99: 40; 100-119: 15; 120-139: 5; 140-159: 1 B. Estimate the total number of children included in the histogram. - 77 children. C. What are the lowest and highest possible IQ scores in the sample according to the histogram? - The lowest possible score in the sample is 40, and the highest possible score in the sample is 160. D. How would the shape of the histogram change if relative frequencies were used instead of frequencies? - The shape of the histogram would not change, because each measure is scaled down by the same amount. E. IQ scores for all children are defined to have an average of score of 100. - Does the histogram provide any evidence to suggest that the high lead levels have affected IQs? - The number of children with scores above 100 is less than the number of children with scores below 100, so the histogram provides evidence that high lead levels lower IQ scores, but does not prove it.

Question 62

Relative Change

Answer 62

Relative change = new value - reference value divided by reference value x 100

Question 63

For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio - The durations of movies in minutes

Answer 63

Ratio

Question 64

For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio The most common names in different countries

Answer 64

Nominal

Question 65

Determine whether the given statement represents a meaningful ratio, so that the ratio level of measurement applies. Explain. One subject has an IQ score of 1580 and another subject has an IQ score of 790, so the first subject is twice as intelligent as the second subject

Answer 65

The ratio level does not apply because the measurement of IQ score has an arbitrary zero point

Question 66

Determine whether the data described below are qualitative or quantitative and also identify their level of measurement. If the data are quantitative, state whether they are continuous or discrete, and give a brief explanation. The types of drinks available at a restaurant

Answer 66

The data are qualitative and are at the nominal level of measurement because the data are not counts or measurements and cannot be ranked - The data are qualitative

Question 67

Determine whether the data described below are qualitative or quantitative and also identify their level of measurement. If the data are quantitative, state whether they are continuous or discrete, and give a brief explanation. Seniority of each nurse at a hospital is based on the time in whole years that has passed since the nurse was first hired

Answer 67

The data are discrete because the years since hiring can only be a whole number

Question 68

One of the authors received a credit card bill for $2,651, but it included a charge of $1,848 that was not valid. Find the values of the absolute and relative errors.

Answer 68

The value of the absolute error is $1848. The value of the relative error is 230%

Question 69

Distinguish between absolute and relative change. Give an example that illustrates how we calculate a relative change.

Answer 69

Absolute change is the actual increase or decrease from a reference value to a new value. - Relative change is the size of a change in comparison to the reference value Suppose your hourly salary is $20, but then you get a raise to $21.25. Illustrate how to calculate the relative change. - The relative change is $21.25 - $20 divided by $20 x 100% =6.25%

Question 70

The following statement provides two values. For the pair of values, use a percentage to express their relative change or difference. Use the second given value as the reference value. Also, write a statement describing the result. The population for a particular region is now 329,647,523, and in 2002 it was 290,616,074.

Answer 70

- The population now is P% more than the population in 2002, where the relative change equals P% - The population increased by the amount of the relative change from 2002 to now

Question 71

Last December there were 647,991 scheduled passenger flights in a certain country, and in December of 1995 there were 742,708. Use a percentage to express the relative change. Use the second given value as the reference value. Also, write a statement describing the result.

Answer 71

The relative difference between December of 1995 and last December is -13% There is a 13% decrease in the number of scheduled passenger flights from December of 1995 to last December.