Core Academic Skills Assessment Mathematics: Data and Statistics 5 — Questions and Answers
Question 1: A line of best fit for a data set is y = 3x + 2. If x = 7, what does the model predict for y?
- 17
- 21
- 23 (Correct answer)
- 27
Correct answer: 23
y = 3(7) + 2 = 21 + 2 = 23.
Question 2: Which measure best describes the spread of a dataset that contains significant outliers?
- Standard deviation
- Range
- IQR (Correct answer)
- Variance
Correct answer: IQR
The IQR is based on the middle 50% of data and is resistant to the influence of outliers.
Question 3: A class of 30 students took a test. The mean score was 72. If 5 more students scored 90 each, what is the new mean?
- 73.33
- 74.57
- 75.14 (Correct answer)
- 76.00
Correct answer: 75.14
Original sum = 30 × 72 = 2160; new sum = 2160 + 5 × 90 = 2610; new mean = 2610 / 35 ≈ 74.57.
Question 4: A cumulative frequency graph (ogive) shows that 60% of students scored below 75. If there are 200 students, how many scored 75 or above?
- 60
- 75
- 80 (Correct answer)
- 120
Correct answer: 80
60% scored below 75, so 40% scored 75 or above; 0.40 × 200 = 80 students.
Question 5: A coin is flipped 3 times. What is the probability of getting exactly 2 heads?
- 1/8
- 2/8
- 3/8 (Correct answer)
- 4/8
Correct answer: 3/8
The combinations for exactly 2 heads (HHT, HTH, THH) = 3 out of 8 equally likely outcomes, so P = 3/8.
Question 6: When comparing two data sets with the same mean, the data set with a larger standard deviation has:
- More data points
- A higher median
- Greater variability (Correct answer)
- Fewer outliers
Correct answer: Greater variability
Standard deviation measures spread; a larger value means data points are more spread out from the mean.
Question 7: A frequency table shows intervals and frequencies. The interval 20–29 has a frequency of 15 and the total sample size is 60. What is the relative frequency for this interval?
- 0.15
- 0.20
- 0.25 (Correct answer)
- 0.30
Correct answer: 0.25
Relative frequency = 15 / 60 = 0.25.
Core Academic Skills Assessment Mathematics: Data and Statistics 5
A line of best fit for a data set is y = 3x + 2.
If x = 7, what does the model predict for y?