##### 1. If you were presented with the following set of numbers representing employee hourly rates, which answer choice would provide the mean, median, and mode of those rates in consecutive order?

###### 10.50, 12.00, 15.00, 12.00, 13.75, 22.00, 13.50

- 14.11, 13.50, 12.00
- 12.00, 13.00, 13.50
- 14.11, 13.50, 22.00
- 13.75, 12.00, 14.50

##### 2. Extrapolation is a process that is reasonably reliable for short term use in:

- creating an equation using only known variables
- calculating the sum of a series of both positive and negative variables
- solving an equation that can have multiple outcomes based on variables
- estimating the value of a variable at an unobserved time or circumstance

##### 3. You are calculating the probability that your department will make its quarterly goals. In statistical calculations, probability is shown as:

- a fraction
- odds against
- a number between zero and one
- all of the above

##### 4. If you travel to Mexico while the exchange rate from U.S. dollars to pesos is $1 = 10.85, what would be your total expenditure in U.S. dollars for two nights in a hotel at 550 pesos per night, six meals at 78 pesos each, and four cab rides at 84 pesos each?

- $101.38
- $116.31
- $144.52
- $175.48

##### 5. After administering a test on computer applications to prospective employees, you consider all test results and decide to interview candidates whose scores were in the 90^{th} percentile or higher. This would be candidates whose scores:

- reflected 90% accuracy or higher
- were better than 90% of the candidates tested
- demonstrated exceptional proficiency in computer applications
- B and C

##### 6. An employee performance appraisal system operates on a 5 point scale with a weighted average based on the following: Supervisor evaluation 50%, co-worker evaluations 10%, employee self evaluation 20%, performance data 20%. What is the weighted average or score for any employee’s performance who receives the following scores: Supervisor – 4.5, co-workers – 4.5, self – 4.25, performance data – 3.75?

- 4.25
- 4.30
- 4.35
- 4.50

##### 7. If simple interest is calculated using the formula A=P(1+nr) where A is total principle and interest, P is principle, n is number of years, and r is rate, what would be the simple interest earned on an investment of $2000.00 at 12.5% for 9 years?

- $4250.00
- $2250.00
- $1250.00
- $250.00

##### 8. If asked to provide the quotient of your division’s clocked work hours (Hours) and the number of division employees (Employees), the answer would be calculated by which of the following formulas?

- Hours + Employees = Quotient
- Hours x Employees = Quotient
- Hours / Employees = Quotient
- (Hours + Employees) / Employees = Quotient

##### 9. Your manager has stated the department goal of increasing annual sales numbers by 23% for the next year. If your year one sales were $17,550,000, in order to meet this goal, your sales in year two must be at least:

- $40,365,000
- $21,586,500
- $58,754,347
- $22,815,000

##### 10. ABC Shoe Company reports annual sales of $4,500,000. If they make a net profit of $300,000, what is the rate of profit?

- 6.7%
- 14%
- 15%
- 33.3%

##### 11. Your organization develops a marketing strategy to reach its target audience by using the science or process of drawing likely conclusions about populations by analyzing samples from that population, known as:

- descriptive statistics
- standard deviations
- inferential statistics
- central tendency

##### 12. Ten candidates for employment earn the following scores on a general aptitude test: 67, 98, 78, 89, 86, 92, 56, 87, 90, 98. If the scores are based on a 100 point scale, what is the range?

- 2
- 10
- 42
- 84

##### 13. If your organization is conducting research to investigate the role that gender plays in obesity related heath problems, out the possible variables considered, which of the following would be considered independent?

- gender
- blood pressure
- weight
- number of annual trips to the doctor

##### 14. You are developing official forms for a target population. In conducting research, you gather data about your target population from a random sample. This data includes race, gender, and family status. This type of variable is known as:

- ordinal
- interval
- ratio
- nominal

##### 15. A computer program that runs an alarm system which automatically notifies the police if a door or window is opened, and 15 seconds pass without the disarm code being entered, is designed using:

- heuristics
- algorithms
- fixed ratios
- standard deviations

##### 16. John works 40 hours in a week, at $15.00 per hour, and produces 150 widgets. Amy works 32 hours in a week, at $18.50 per hour, and produces 128 widgets. Dave works 36 hours in a week, at $17.75 per hour, and produces 141 widgets. Which employee is the most cost effective for the company in terms of widgets produced per dollar of payroll spent?

- John
- Amy
- Dave
- Dave and Amy are equally effective

##### 17. Which of the following formulas would accurately calculate the probability of an event occurring?

- Probability = Total number of ways event can occur / Total number of possible outcomes
- Probability = Total number of possible outcomes / Total number of ways event can occur
- Probability = (Total number of ways event can occur – Total number of possible outcomes) / Total number of possible outcomes
- Probability = (Total number of ways event can occur + Total number of possible outcomes) / Total number of ways event can occur

##### 18. You are purchasing some rope for a project. The directions indicate that you will need 23.5 meters. If you convert this to a commonly used unit of measurement in the United States, you will need to buy:

- approximately 75.5 feet
- exactly 141 feet
- approximately 35.25 yards
- exactly 23.5 yards

##### 19. If you are traveling 100 miles in a vehicle that gets 30 mpg, how many liters of gas would you need if the conversion ratio for a gallon to a liter is 1 = 3.785?

- 1.136
- 12.617
- 113.550
- 348.500

##### 20. Which of the following would not be considered a digit?

- 0
- 1
- 9
- 99

##### 21. In a math problem such as {(3546-2345) X (3567/23.4)} / (349 + 1256), order of operations defines in which order different operations must be completed. Which would come first?

- Addition
- Multiplication
- Brackets
- Parenthesis

##### 22. You are measuring a large dirt field in order to purchase exactly enough grass sod to cover it. One section is a triangular shape. Which of the following formulas where A = area would you use to calculate that section?

- A = L’
- A = B X H
- A = ½ B X H
- A = L X W

##### 23. Your division employs 5300 employees. 15% of these employees are considered management level. How many employees does your division have in the non-management category?

- 795
- 850
- 1500
- 4505

##### 24. You are driving to a meeting 890 miles away and have estimated an average travel rate of 60 mph. Approximately how long will it take you to reach your destination?

- 14 hours
- 15 hours
- 7 hours
- 21 hours

##### 25. The first 12% of a project has been completed at a total cost of $850,000. The project managers have calculated that the remainder of the project should be completed at a similar dollar per percentage rate. Approximately how much should the entire project cost?

- $960,000
- $1,600,000
- $6,000,000
- $7,000,000

##### 26. You calculate the value of a $10,000 investment compounded continuously at 8% for 10 years. The result would be an example of:

- exponential growth
- ratio analysis
- simple interest
- quotients

##### 27. Your firm conducted an advertising campaign to reach a target audience of young people ages 14 to 25. The campaign was designed using information about the target audience gathered in a statistical study of a random sample from this larger population. The campaign failed to reach the target audience effectively, due perhaps to:

- using too small of a sample size
- misinterpretation of data
- the use of qualitative data
- A and B

##### 28. When compiling statistical data on the performance appraisals of your employees you examine the set of raw rating scale scores and discover that it is multimodal meaning:

- it contains all possible scores from the lowest to the highest
- several scores are repeated in the set
- no scores are repeated or duplicated among employees
- the scores follow a distinct pattern of performance

##### 29. Annual raises in your department were determined by a merit system and have been noted in the following chart. What is the approximate average salary increase in your department?

Employee | Original Salary | New Salary |

John | $48,000 | $52,000 |

Jane | $54,000 | $60,000 |

Jim | $37,000 | $47,000 |

Jill | $68,000 | $75,000 |

Jeff | $78,000 | $89,000 |

- 8%
- 10%
- 14%
- 18%

##### 30. Your departmental budget for last year was $765,000. You budget for this year reflects a 15% increase. You have decided to use 85% of the increase to add additional personnel. Which of the following scenarios would fit into your budget and use the largest portion of the available funds?

- You decide to hire two additional clerks at annual salaries of $28,000 each and one additional analyst at a salary of $40,000
- You decide to hire two additional analysts at a salary of $38,000 each and one additional secretary at an annual salary of $39,000
- You decide to hire two additional clerks and two additional secretaries each at annual salaries of $28,500.
- You decide to hire three additional analysts each at an annual salary of$36,500.

##### 31. You are presented with a list of material measurements for a project from Germany. All materials are listed in metric measurements. What would be the most comparable measurement for materials described in kilograms:

- inches
- pounds
- quarts
- tons

##### 32.During the previous year, 110 on the job accidents were reported. Your department has established a goal of decreasing the total number of on the job accidents by 75%. During the next year, 82 accidents are reported. How did your department perform in relation to your goal?

- The department achieved the goal with a 75% reduction in accidents
- The department achieved the goal with an 80% reduction in accidents
- The department missed the goal with only a 34% reduction in accidents
- The department missed the goal with only a 25% reduction in accidents

##### 33.You have been asked to compile statistical data about your employee’s performance evaluations. You used a ranking scale of 1 to 20 for one aspect of this appraisal. You consider the following scores – 19, 15,16, 10, 15, 15, 18, 20, 20, 18 – and determine that the median score is:

- 10
- 15
- 16.6
- 17

##### 34. A business trip takes you to several European countries during a six day period.Your business expenses for this trip are $1350.00. Assuming equal daily expenditures and an exchange rate of $1 = 0.850 euros, approximately how many euros did you spend each day?

- 191
- 225
- 265
- 321

##### 35.If your flight departs New York at 10:00 AM and lands in Los Angeles five hours later, what time would it be in Los Angeles?

- 10:00 AM
- 11:00 AM
- 12:00 PM
- 1:00 PM

##### 36.If your organization is considering all Americans registered to vote as the population for statistical study, the percentage of those Americans who intend to vote in the upcoming national elections would be considered:

- a sample
- a parameter
- a deviation
- a quotient

##### 37. When analyzing the performance of each division in your organization in regards to sales quotas, you would look at the standard deviation of each division to determine:

- the mean performance of all divisions
- how far apart the divisions are from the mean
- what level of performance was most commonly occurring
- the lowest and highest performing divisions

##### 38.You are considering organizing your staff into teams to tackle upcoming projects. When looking at the permutations of team organization, you are considering:

- how many teams can be effectively created
- how many people should be on each team
- how many ways people can be organized into teams
- how many projects can be tackled at one time

##### 39.You are analyzing the relationship between employees working more than ten hours in a shift and the number of on the job accidents at your production facility. One aspect to consider is the relative frequency which would be:

- the total number of accidents divided by the number of times employees worked more than ten hours in a shift
- the number of times employees worked more than ten hours in a shift divided by the total number of accidents
- the number of times employees worked more than ten hours in a shift minus the total number of accidents divided by the number of times employees worked more than ten hours in a shift
- The total number of accidents times the number of times employees worked more than ten hours in a shift divided by the total number of accidents.

##### 40.Your department consists of twelve employees and your total payroll expense for salaries only is $325,000. The organization’s average salary is $36,000. What is the relation of your department’s average salary to the organization’s average?

- Your department is about 25% below average
- Your department is about 30% below average
- Your department is about 25% above average
- Your department is about 30% above average

**FSOT Mathematics – Answer Key**

###### 1. A.

Mean represents the sum of all rates divided by the total number of rates. Median represents the number below and above which an equal number of numbers fall. Mode represents the most frequently occurring number.

###### 2. D.

definition

###### 3. D.

Probability is traditionally shown as a number between 0 and 1. For example when tossing a coin, the probability of heads and tails are equal at 0.5. However, it can also be shown as odds against or as a fraction.

###### 4. D.

Add all expenditures in pesos. Divide by 10.85 to convert back to American dollars.

###### 5. B.

Percentile ranking indicates the percentage of scores that ranking is above. A 90th percentile ranking means that score was higher than 90% of scores. This alone cannot be construed as proficient since it is only a measure of comparison, not a measure of performance to standards.

###### 6. B.

Weighed average would be calculated with this formula: (0.50)(4.5) + (0.10)(4.5) + (0.20)(4.25) + (0.20)(3.75) = Employee score

###### 7. B.

Apply numbers to formula to find that A=$4250.00. Subtract principle amount of $2000.00 to find simple interest earned.

###### 8. C.

Quotient is the result of division of one number into another.

###### 9. B.

Portion or year two sales = base or year one sales x rate. Rate is 123% or 1.23.

###### 10. A.

Rate = Portion or profit / base or total sales. Rate = 300,000/4,500,000.

###### 11. C.

definition

###### 12. C.

Range is the difference between the highest and lowest numbers in a set. In this case, the 100 point scale is irrelevant.

###### 13. A.

Independent variables are those that are manipulated in research or those variables used to assign subjects to experimental groups. Dependent variables are those that are simply measured or recorded.

###### 14. D.

Nominal variables are qualitative in nature and can not be quantified. Interval, ratio, and ordinal variables are all quantifiable in nature.

15. B.

Algorithms are a precise set of operations or steps that produce a specific result. Example: 1. Door opens 2. 5 seconds pass 3. No code entered = Police notified

###### 16. A.

Total hours worked X hourly rate / widgets produced = widget per payroll dollar. John was $4/widget making him the most cost effective. Amy was $4.625/widget and Dave was $4.453/widget.

###### 17. A.

This is the basic formula for determining probability of an event occurring.

###### 18. A.

This is the best choice. The approximate conversion commonly used is 1 meter = about 1 yard. Exact is 1 = 1.0936… The approximate conversion commonly used is 1 meter = about 3 feet. Exact is 1 = 3.281.

###### 19. B.

Divide 100 by 30 to determine gallons needed = 3.33333. Multiply times 3.785 = 12.617.

###### 20. D.

Digits are only 0,1,2,3,4,5,6,7,8,9.

###### 21. C.

The order is Brackets, Parenthesis, Exponents, Multiplication or Division, Addition or Subtraction.

###### 22. C.

The area of a triangle is calculated by ½ base times height.

###### 23. D.

This can be calculated by determining 15% of 5300 (5300 X 0.15) which equals 795 and subtracting that from 5300 or by simply calculating 85% of 5300 (5300 X 0.85).

###### 24. B.

Rate = distance / time. Rate = 890 /60. Rate = 14.8

###### 25. D.

Total cost = 850,000/0.12 which equals 7,083,333.

###### 26. A.

Exponential growth is defined as that growth which is in direct proportion to amount present as is true with an investment in which interest is compounded continuously.

###### 27. D.

The simple fact of using qualitative data would not be reason enough to declare a statistical study ineffective. However, using too small of a sample can prevent your data from accurately reflecting the total population. Additional, misleading or misapplication of percentages, ratios, etc. can create inaccurate data about the total population as well.

###### 28. B.

Mode is the value in a set that appears most frequently. Bimodal or multimodal means there is more than one mode.

###### 29. C.

Calculate individual percentage raises by subtracting old salary from new salary, dividing the difference by the old salary, and dividing by 100. Add all percentage raises together and divide by 5.

###### 30. A.

Calculate total budget increase as 765,000 X 0.15 = 114,750. Calculate amount available for additional personnel as 114,750 X 0.85 = 97,538.

###### 31. B.

A kilogram is a measure of weight or mass and equals approximately 2.2 pounds. Although tons also measure weight or mass, it is a much larger tool. Inches measure length or distance and quarts measure volume.

###### 32. D.

Calculate reduction percentage as old number minus new number divided by old number times 100. 110 – 82 = 28 / 100 = 0.25 X 100 = 25%

###### 33. D.

Median is the middle number of a set of numbers arranged by size. If there are two middle numbers as with a set with an even number, the median is the mean or average of those numbers.

###### 34. A.

Multiply $1350 by 0.850 which equals 1148. Divide this by 6 for the daily rate.

###### 35. C.

There is a three hour difference between New York in EST and Lost Angeles in PST. Subtract three hours from 10:00 to obtain PST when flight departs and then add the five hour flight time to determine arrival time.

###### 36. A.

A parameter is a numerical measurement of one characteristic or quality of the population being studied.

###### 37. B.

Standard deviation is a common way to measure the statistical dispersion of data, or in other words, how spread out each is from the mean.

###### 38. C.

A permutation is the number of different ways a set of objects can be arranged.

###### 39. A.

Relative frequency can be described as the number of times an event occurs divided by the number of opportunities it had to occur.

###### 40. A.

$325,000 divided by 12 equals an average salary of about $27,000. This is $9,000 below the organization’s average of $36,000. $9000 divided by $36,000 equals 0.25 times 100 equals 25%.