NBT Statistics and Probability 2 — Questions and Answers
Question 1: What is the range of the data set: 5, 8, 12, 3, 15, 7?
- 10
- 12 (Correct answer)
- 15
- 8
Correct answer: 12
Range = maximum - minimum = 15 - 3 = 12. The range gives a simple measure of how spread out the data is.
Question 2: A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability it is blue?
- 3/5
- 3/8 (Correct answer)
- 5/8
- 1/3
Correct answer: 3/8
Total balls = 5 + 3 = 8. P(blue) = number of blue balls ÷ total = 3/8. Each ball has an equal chance of being drawn.
Question 3: The standard deviation measures:
- The central value of a data set
- The spread of data around the mean (Correct answer)
- The most common value
- The difference between highest and lowest values
Correct answer: The spread of data around the mean
Standard deviation measures how spread out data values are around the mean. A small standard deviation means data points cluster near the mean; a large one means they are more spread out.
Question 4: If a coin is tossed 3 times, what is the probability of getting exactly 2 heads?
- 1/4
- 3/8 (Correct answer)
- 1/2
- 1/8
Correct answer: 3/8
The possible outcomes with exactly 2 heads are: HHT, HTH, THH — that's 3 outcomes out of 2³ = 8 total. P = 3/8.
Question 5: What is the interquartile range (IQR) if Q1 = 15 and Q3 = 35?
- 50
- 20 (Correct answer)
- 25
- 15
Correct answer: 20
IQR = Q3 - Q1 = 35 - 15 = 20. The IQR measures the spread of the middle 50% of the data and is resistant to outliers.
Question 6: Two events are mutually exclusive if:
- They always occur together
- They cannot occur at the same time (Correct answer)
- One event causes the other
- They have the same probability
Correct answer: They cannot occur at the same time
Mutually exclusive events cannot occur simultaneously. If one happens, the other cannot. For example, getting heads and tails on a single coin flip are mutually exclusive.
NBT Statistics and Probability 2
What is the range of the data set: 5, 8, 12, 3, 15, 7?