NJGPA Statistics, Data Analysis, and Probability 2 — Questions and Answers
Question 1: A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning an even number?
- 1/4
- 3/8
- 1/2 (Correct answer)
- 5/8
Correct answer: 1/2
The even numbers are 2, 4, 6, and 8 — that's 4 out of 8 sections, giving a probability of 4/8 = 1/2.
Question 2: A frequency table shows that 12 students scored in the 80–89 range out of 40 total students. What percentage of students scored in this range?
- 12%
- 25%
- 30% (Correct answer)
- 33%
Correct answer: 30%
12 ÷ 40 = 0.30, and 0.30 × 100 = 30%, so 30% of students scored in the 80–89 range.
Question 3: Two events are independent if the outcome of one does not affect the outcome of the other. A fair coin is flipped twice. What is the probability of getting heads both times?
- 1/4 (Correct answer)
- 1/2
- 3/4
- 1/3
Correct answer: 1/4
Each flip has a 1/2 probability of heads; since the flips are independent, multiply: 1/2 × 1/2 = 1/4.
Question 4: Which graphical display is best for showing how a single data set is distributed, including the median and quartiles?
- Pie chart
- Line graph
- Box plot (Correct answer)
- Histogram
Correct answer: Box plot
A box plot (box-and-whisker plot) directly displays the minimum, Q1, median, Q3, and maximum of a data set.
Question 5: A data set of test scores has a mean of 78 and a standard deviation of 5. Which score is closest to 2 standard deviations above the mean?
- 83
- 85
- 88 (Correct answer)
- 90
Correct answer: 88
Two standard deviations above the mean: 78 + 2(5) = 78 + 10 = 88.
Question 6: A survey asks 200 people whether they prefer coffee or tea. 130 prefer coffee. What is the relative frequency of people who prefer tea?
- 0.35 (Correct answer)
- 0.45
- 0.65
- 0.70
Correct answer: 0.35
70 people prefer tea (200 − 130 = 70), and 70 ÷ 200 = 0.35.
Question 7: A line of best fit on a scatter plot has the equation y = 2x + 3. What does the slope of 2 represent in context?
- The starting value of y when x equals zero
- For every 1-unit increase in x, y decreases by 2
- For every 1-unit increase in x, y increases by 2 (Correct answer)
- The value of x when y equals zero
Correct answer: For every 1-unit increase in x, y increases by 2
The slope represents the rate of change; a slope of 2 means y increases by 2 for each 1-unit increase in x.
NJGPA Statistics, Data Analysis, and Probability 2
A spinner has 8 equal sections numbered 1 through 8.
What is the probability of spinning an even number?