Q.1 What is the mean of the data set: 2, 4, 6, 8, 10?
4
5
6
7
Explanation - The mean is calculated as the sum of all values divided by the number of values: (2+4+6+8+10)/5 = 30/5 = 6.
Correct answer is: 6
Q.2 Which of the following is a measure of data dispersion?
Mean
Median
Variance
Mode
Explanation - Variance measures how much the data points deviate from the mean, which is a measure of dispersion.
Correct answer is: Variance
Q.3 In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?
50%
68%
95%
99%
Explanation - In a normal distribution, about 68% of the data falls within ±1 standard deviation of the mean.
Correct answer is: 68%
Q.4 The median of the data set 3, 7, 9, 12, 15 is:
7
9
10
12
Explanation - Median is the middle value when the data is arranged in ascending order. Here, the middle value is 9.
Correct answer is: 9
Q.5 If P(A) = 0.3 and P(B) = 0.4, assuming A and B are independent, what is P(A ∩ B)?
0.12
0.7
0.1
0.3
Explanation - For independent events, P(A ∩ B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
Correct answer is: 0.12
Q.6 Which of the following is a categorical variable?
Age
Height
Gender
Weight
Explanation - Categorical variables represent categories or groups. Gender is an example, while age, height, and weight are numerical.
Correct answer is: Gender
Q.7 In a probability distribution, the sum of all probabilities must be:
0
1
Less than 1
Greater than 1
Explanation - The total probability of all outcomes in a probability distribution must equal 1.
Correct answer is: 1
Q.8 Which plot is most suitable for visualizing the frequency of categories?
Histogram
Pie Chart
Scatter Plot
Line Graph
Explanation - Pie charts are used to represent categorical data as proportions of a whole.
Correct answer is: Pie Chart
Q.9 The variance is the square of which statistical measure?
Mean
Standard Deviation
Median
Mode
Explanation - Variance is defined as the square of the standard deviation.
Correct answer is: Standard Deviation
Q.10 If the correlation coefficient between two variables is -0.85, it indicates:
Strong positive correlation
Weak positive correlation
Strong negative correlation
No correlation
Explanation - A correlation coefficient close to -1 indicates a strong negative correlation between the variables.
Correct answer is: Strong negative correlation
Q.11 A random variable that can take only integer values is called:
Continuous
Discrete
Categorical
Nominal
Explanation - Discrete random variables take countable integer values, while continuous variables can take any value within a range.
Correct answer is: Discrete
Q.12 The mode of the data set 1, 2, 2, 3, 3, 3, 4 is:
2
3
4
2 and 3
Explanation - Mode is the value that appears most frequently. Here, 3 appears three times, more than any other value.
Correct answer is: 3
Q.13 Which of the following distributions is symmetric?
Poisson
Exponential
Normal
Binomial with p ≠ 0.5
Explanation - The normal distribution is perfectly symmetric about its mean.
Correct answer is: Normal
Q.14 In a box plot, what does the box represent?
Mean ± SD
Interquartile Range
Minimum to Maximum
Median only
Explanation - The box in a box plot represents the interquartile range (IQR), which contains the middle 50% of data.
Correct answer is: Interquartile Range
Q.15 The probability of an impossible event is:
0
0.5
1
Undefined
Explanation - By definition, an impossible event has probability 0.
Correct answer is: 0
Q.16 If a dataset has mean 50 and standard deviation 5, what is the z-score of 55?
1
0.5
5
10
Explanation - Z-score = (X - mean)/SD = (55-50)/5 = 1.
Correct answer is: 1
Q.17 A positively skewed distribution has:
Mean < Median < Mode
Mode < Median < Mean
Mean = Median = Mode
Median > Mean > Mode
Explanation - In a positively skewed distribution, the tail is on the right, so mean > median > mode.
Correct answer is: Mode < Median < Mean
Q.18 Which measure is least affected by outliers?
Mean
Median
Variance
Range
Explanation - Median is the middle value and is less sensitive to extreme values compared to mean, variance, or range.
Correct answer is: Median
Q.19 If events A and B are mutually exclusive, P(A ∪ B) equals:
P(A) × P(B)
P(A) + P(B)
P(A) - P(B)
1 - P(A)
Explanation - For mutually exclusive events, P(A ∪ B) = P(A) + P(B) because they cannot occur together.
Correct answer is: P(A) + P(B)
Q.20 Which of the following is a continuous random variable?
Number of students
Time to run a race
Number of cars
Number of defects
Explanation - Continuous random variables can take any value within a range, e.g., time, distance, weight.
Correct answer is: Time to run a race
Q.21 The coefficient of variation (CV) is calculated as:
Mean / SD
SD / Mean
Mean × SD
SD - Mean
Explanation - CV = (Standard Deviation / Mean) × 100%, and it measures relative variability.
Correct answer is: SD / Mean
Q.22 The probability distribution of a single trial with two outcomes is called:
Binomial
Poisson
Normal
Geometric
Explanation - A binomial distribution models the number of successes in a fixed number of independent trials with two outcomes.
Correct answer is: Binomial
Q.23 Which of the following is true for the standard normal distribution?
Mean = 0, SD = 1
Mean = 1, SD = 0
Mean = 0, SD = 0
Mean = 1, SD = 1
Explanation - By definition, the standard normal distribution has a mean of 0 and standard deviation of 1.
Correct answer is: Mean = 0, SD = 1
Q.24 Which plot is best for showing trends over time?
Bar Chart
Histogram
Line Graph
Pie Chart
Explanation - Line graphs are ideal for visualizing data trends over a continuous interval, such as time.
Correct answer is: Line Graph
Q.25 The expected value of a discrete random variable X is:
Sum of all outcomes
Sum of probabilities
Weighted average of outcomes
Maximum outcome
Explanation - Expected value is the sum of each outcome multiplied by its probability, i.e., the weighted average.
Correct answer is: Weighted average of outcomes