Core Academic Skills Assessment Mathematics: Data and Statistics 4 — Questions and Answers
Question 1: A data set has a mean of 50 and a standard deviation of 5. A value of 60 has a z-score of:
- 1
- 2 (Correct answer)
- 5
- 10
Correct answer: 2
z = (60 − 50) / 5 = 10 / 5 = 2.
Question 2: The correlation coefficient between study hours and test scores is r = 0.92. This means:
- Study hours cause higher scores
- There is a strong positive linear relationship (Correct answer)
- 92% of students studied
- The data has 92 points
Correct answer: There is a strong positive linear relationship
A correlation coefficient close to +1 indicates a strong positive linear relationship between the two variables.
Question 3: Which of the following correctly identifies a potential source of bias in a survey?
- Using a large sample size
- Randomly selecting respondents
- Only surveying people who volunteer (Correct answer)
- Including multiple answer choices
Correct answer: Only surveying people who volunteer
Voluntary response bias occurs when only those who choose to participate are included, skewing results toward those with strong opinions.
Question 4: A dataset: 2, 5, 5, 6, 8, 9, 11, 15. A value of 25 is added. How does this affect the median?
- The median increases by about 8.5
- The median stays the same
- The median increases slightly (Correct answer)
- The median decreases
Correct answer: The median increases slightly
With 8 values the median is (6+8)/2=7; with 9 values it is the 5th value = 8, a slight increase.
Question 5: On a pie chart representing a budget of $2,000, the 'food' sector has a central angle of 72°. How much is budgeted for food?
- $200
- $360
- $400 (Correct answer)
- $720
Correct answer: $400
72° / 360° = 0.20; 0.20 × $2,000 = $400.
Question 6: A survey of 200 people finds 80 prefer Brand A. What is the relative frequency of people who prefer Brand A?
- 0.30
- 0.40 (Correct answer)
- 0.45
- 0.80
Correct answer: 0.40
Relative frequency = 80 / 200 = 0.40.
Question 7: Two events A and B are mutually exclusive. P(A) = 0.4 and P(B) = 0.25. What is P(A or B)?
- 0.10
- 0.15
- 0.65 (Correct answer)
- 0.75
Correct answer: 0.65
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.25 = 0.65.
Core Academic Skills Assessment Mathematics: Data and Statistics 4
A data set has a mean of 50 and a standard deviation of 5.
A value of 60 has a z-score of: