ISAT Probability and Statistical Analysis 4 — Questions and Answers
Question 1: The interquartile range (IQR) is defined as:
- Q3 − Q1 (Correct answer)
- Q2 − Q1
- Max − Min
- Q3 − Q2
Correct answer: Q3 − Q1
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1), representing the middle 50% of data.
Question 2: A student draws 2 cards from a standard 52-card deck without replacement. What is the probability both are aces?
- 1/169
- 1/221 (Correct answer)
- 4/52
- 1/13
Correct answer: 1/221
P = (4/52) × (3/51) = 12/2652 = 1/221.
Question 3: Which of the following best describes a positively skewed distribution?
- Mean = Median = Mode
- Mean < Median < Mode
- Mean > Median > Mode (Correct answer)
- Mode > Mean > Median
Correct answer: Mean > Median > Mode
In a positively (right) skewed distribution, the tail extends right, pulling the mean above the median, which is above the mode.
Question 4: A jar has 5 white and 3 black balls. What is the probability of drawing a black ball on the second draw, given the first draw was white (without replacement)?
- 3/8
- 3/7 (Correct answer)
- 5/8
- 1/2
Correct answer: 3/7
After removing a white ball, 7 remain (4 white, 3 black); P(black) = 3/7.
Question 5: A frequency table shows 5 classes. Which statistical tool best displays this data visually?
- Scatter plot
- Box-and-whisker plot
- Histogram (Correct answer)
- Line graph
Correct answer: Histogram
A histogram displays the distribution of data across intervals (classes), making frequency tables easy to visualize.
Question 6: A die is rolled twice. What is the probability that the sum equals 7?
- 1/6 (Correct answer)
- 7/36
- 1/12
- 6/36
Correct answer: 1/6
Pairs that sum to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 out of 36 total outcomes = 1/6.
Question 7: Standard deviation measures:
- The most common value in a dataset
- The average distance of data points from the mean (Correct answer)
- The difference between max and min values
- The middle value of a dataset
Correct answer: The average distance of data points from the mean
Standard deviation quantifies how spread out data points are around the mean on average.
ISAT Probability and Statistical Analysis 4
The interquartile range (IQR) is defined as: