NBT NBT Statistics and Probability 5 — Questions and Answers
Question 1: A scatter plot shows a strong negative correlation. Which statement best describes this relationship?
- As x increases, y increases
- As x increases, y decreases (Correct answer)
- There is no relationship between x and y
- As x decreases, y decreases
Correct answer: As x increases, y decreases
A negative correlation means that as one variable increases, the other decreases.
Question 2: In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical rule states that approximately 68% of data falls within one standard deviation of the mean.
Question 3: A bag has 6 red and 4 blue chips. Two chips are drawn without replacement. What is the probability both are red?
- 1/3 (Correct answer)
- 36/100
- 6/15
- 1/2
Correct answer: 1/3
P(both red) = (6/10) × (5/9) = 30/90 = 1/3.
Question 4: Which of the following correctly describes a frequency histogram?
- A pie chart divided into equal sectors
- A bar graph where bars represent frequency of data intervals (Correct answer)
- A line graph showing data over time
- A scatter plot of two variables
Correct answer: A bar graph where bars represent frequency of data intervals
A frequency histogram uses bars whose heights represent how often data values fall within each interval.
Question 5: The variance of a dataset measures:
- The most common value in the dataset
- The middle value when data is ordered
- The average squared deviation from the mean (Correct answer)
- The difference between the largest and smallest values
Correct answer: The average squared deviation from the mean
Variance is the mean of the squared differences between each data point and the overall mean.
Question 6: If P(A) = 0.4 and P(B) = 0.5 and A and B are independent events, what is P(A and B)?
- 0.9
- 0.1
- 0.2 (Correct answer)
- 0.45
Correct answer: 0.2
For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.
Question 7: A stem-and-leaf plot shows: 1|3 5 7, 2|1 4 6 9. What is the median of this dataset?
- 17
- 21 (Correct answer)
- 15
- 24
Correct answer: 21
The 7 ordered values are 13,15,17,21,24,26,29; the median is the 4th value = 21.
NBT NBT Statistics and Probability 5
A scatter plot shows a strong negative correlation.
Which statement best describes this relationship?