CSPA Statistics and Probability Questions and Answers — Questions and Answers
Question 1: A customer service representative handled the following number of calls over a five-day work week: 25, 30, 22, 28, and 30. What was the mean number of calls handled per day?
- 30
- 28
- 27 (Correct answer)
- 22
Correct answer: 27
The mean is the sum of all values divided by the number of values. The sum of the calls is 25 + 30 + 22 + 28 + 30 = 135. There are 5 data points (days). The mean is 135 ÷ 5 = 27.
Question 2: A team consists of 7 members with the following ages: 24, 45, 28, 33, 28, 51, 38. What is the median age of the team members?
- 28
- 35.3
- 51
- 33 (Correct answer)
Correct answer: 33
The median is the middle value in a data set when it is ordered from least to greatest. First, order the ages: 24, 28, 28, 33, 38, 45, 51. In this set of 7 numbers, the middle value is the 4th one, which is 33.
Question 3: A quality control inspector checks a batch of 200 light bulbs and finds that 8 are defective. If one light bulb is selected at random from the batch, what is the probability that it is defective?
- 1 in 200
- 8%
- 4% (Correct answer)
- 1 in 25
Correct answer: 4%
Probability is calculated by dividing the number of favorable outcomes (defective bulbs) by the total number of possible outcomes (all bulbs). Here, there are 8 defective bulbs and 200 total bulbs. The probability is 8/200. To express this as a percentage, simplify the fraction to 2/50 or 1/25, which is 0.04. Multiply by 100 to get 4%.
Question 4: A project manager for an outdoor construction site records the daily high temperatures (in Celsius) for a week. The recorded temperatures were: 15°C, 18°C, 12°C, 21°C, 20°C, 17°C, and 14°C. What is the range of these temperatures?
- 17°C
- 9°C (Correct answer)
- 21°C
- 12°C
Correct answer: 9°C
The range is the difference between the highest and lowest values in a data set. The highest temperature recorded is 21°C and the lowest is 12°C. The range is calculated as 21 - 12 = 9°C.
Question 5: Review the following sales data for a small business: - January: $12,000 - February: $15,000 - March: $14,000 - April: $18,000 Which of the following statements is a correct interpretation of the data?
- The largest month-over-month sales increase occurred between March and April. (Correct answer)
- Sales consistently increased every month.
- The total sales for the four-month period were less than $55,000.
- February was the month with the highest sales.
Correct answer: The largest month-over-month sales increase occurred between March and April.
To find the largest month-over-month increase, calculate the change for each period: Jan to Feb was a $3,000 increase. Feb to Mar was a $1,000 decrease. Mar to Apr was a $4,000 increase. The $4,000 increase between March and April was the largest. The other statements are incorrect.
Question 6: A company notices that departments that invested more in new computer hardware also reported higher employee productivity. Which of the following is the most reasonable conclusion from this observation?
- The new hardware directly and solely caused the increase in productivity.
- Higher productivity caused the company to invest in new hardware for those departments.
- There is a positive correlation between investment in new hardware and employee productivity. (Correct answer)
- There is no relationship between hardware investment and productivity.
Correct answer: There is a positive correlation between investment in new hardware and employee productivity.
The observation shows that two variables (hardware investment and productivity) tend to increase together, which defines a positive correlation. However, this does not prove that one caused the other (causation). Other factors could be involved. Stating there is a correlation is the only conclusion directly supported by the data without making unproven assumptions.
CSPA Statistics and Probability Questions and Answers
A customer service representative handled the following number of calls over a five-day work week: 25, 30, 22, 28, and 30.
What was the mean number of calls handled per day?