Probability, Sampling Techniques & Data Presentation

Question No. 1 Marks +1 -0 Time

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What is the primary characteristic that distinguishes a mutually exclusive event from an independent event in probability?

A. Mutually exclusive events can never occur together, while independent events do not influence each other's occurrence.
B. Independent events have a joint probability of zero, while mutually exclusive events have a non-zero joint probability.
C. Mutually exclusive events are always dependent, whereas independent events can sometimes be mutually exclusive.
D. The occurrence of one mutually exclusive event increases the probability of the other, which is not true for independent events.

Question No. 2 Marks +1 -0 Time

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Which of the following sampling methods is most likely to suffer from undercoverage bias if the sampling frame is incomplete or outdated?

A. Stratified random sampling
B. Simple random sampling
C. Cluster sampling
D. All of the above are equally susceptible if the sampling frame is flawed.

Question No. 3 Marks +1 -0 Time

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A researcher wants to display the distribution of ages within a population, grouped into 5-year intervals, and wants to visually identify the mode and the overall shape of the distribution. Which graphical representation would be most appropriate?

A. Pie chart
B. Bar chart
C. Histogram
D. Scatter plot

Question No. 4 Marks +1 -0 Time

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Consider two events, A and B. If P(A) = 0.6, P(B) = 0.5, and P(A U B) = 0.8, what can be concluded about events A and B?

A. They are mutually exclusive.
B. They are independent.
C. They are neither mutually exclusive nor independent.
D. They are dependent but not mutually exclusive.

Question No. 5 Marks +1 -0 Time

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Match the following sampling techniques with their primary characteristics:

Sampling Technique	Characteristic
1. Stratified Sampling	P. Every k-th element is selected after a random start.
2. Systematic Sampling	Q. Population is divided into non-overlapping groups, and a random sample is taken from each group.
3. Cluster Sampling	R. Entire groups are randomly selected, and all individuals within the selected groups are studied.
4. Quota Sampling	S. Non-probability method where selection continues until specific proportions of subgroups are met.

Which of the following pairings is correct?

A. 1-Q, 2-P, 3-R, 4-S
B. 1-P, 2-Q, 3-R, 4-S
C. 1-Q, 2-R, 3-P, 4-S
D. 1-S, 2-P, 3-Q, 4-R

Question No. 6 Marks +1 -0 Time

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When comparing the means of two independent groups, which type of plot is typically used to visually assess the overlap and spread of their distributions?

A. Scatter plot
B. Line graph
C. Box plot
D. Bar chart

Question No. 7 Marks +1 -0 Time

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What is the term for the probability of an event occurring, given that another event has already occurred?

A. Joint probability
B. Marginal probability
C. Conditional probability
D. Compound probability

Question No. 8 Marks +1 -0 Time

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Arrange the following steps for conducting a stratified random sample in the correct chronological order:

Define the population and the sampling frame.
Determine the sample size for each stratum.
Divide the population into mutually exclusive and exhaustive strata.
Select a simple random sample from each stratum.

Which of the following sequences is correct?

A. 1, 3, 2, 4
B. 1, 2, 3, 4
C. 3, 1, 2, 4
D. 1, 3, 4, 2

Question No. 9 Marks +1 -0 Time

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If a dataset's histogram shows a long tail to the right, what does this typically indicate about the distribution?

A. It is negatively skewed.
B. It is positively skewed.
C. It is symmetrical.
D. It has a platykurtic distribution.

Question No. 10 Marks +1 -0 Time

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Consider the following statements regarding probability:

Pair 1: The sum of probabilities of all possible outcomes in a sample space is always 1.
Pair 2: If P(A|B) = P(A), then events A and B are mutually exclusive.
Pair 3: An event with a probability of 0.5 is considered a 'certain' event.
Pair 4: The probability of an impossible event is 0.

How many of the above pairs are correct?

A. 1
B. 2
C. 3
D. 4

Question No. 11 Marks +1 -0 Time

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Which sampling method involves dividing the population into groups (clusters) and then randomly selecting some of these clusters, with all individuals within the selected clusters being included in the sample?

A. Stratified random sampling
B. Systematic sampling
C. Simple random sampling
D. Cluster sampling

Question No. 12 Marks +1 -0 Time

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Which measure of central tendency is most affected by extreme outliers in a dataset?

A. Mean
B. Median
C. Mode
D. All are equally affected.

Question No. 13 Marks +1 -0 Time

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If a fair six-sided die is rolled, what type of probability is used to determine the chance of rolling a 3?

A. Empirical probability
B. Subjective probability
C. Classical probability
D. Conditional probability

Question No. 14 Marks +1 -0 Time

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A survey aims to understand the opinions of students in a large university. Researchers decide to interview every 50th student entering the main library on a specific day. What type of sampling technique is this?

A. Simple random sampling
B. Stratified random sampling
C. Systematic sampling
D. Convenience sampling

Question No. 15 Marks +1 -0 Time

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Match the following data types with their appropriate characteristics:

Data Type	Characteristic
1. Nominal Data	P. Categories with a meaningful order, but unequal intervals.
2. Ordinal Data	Q. Categories with no inherent order.
3. Interval Data	R. Ordered data with equal intervals, but no true zero point.
4. Ratio Data	S. Ordered data with equal intervals and a true zero point.

Which of the following pairings is correct?

A. 1-P, 2-Q, 3-R, 4-S
B. 1-Q, 2-P, 3-R, 4-S
C. 1-Q, 2-R, 3-P, 4-S
D. 1-S, 2-R, 3-P, 4-Q

Question No. 16 Marks +1 -0 Time

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Bayes' Theorem is primarily used to:

A. Calculate the probability of the union of two events.
B. Determine the independence of two events.
C. Update the probability of an event based on new evidence.
D. Find the probability of mutually exclusive events.

Question No. 17 Marks +1 -0 Time

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What type of bias occurs when participants in a study alter their behavior because they know they are being observed?

A. Selection bias
B. Response bias
C. Observer bias
D. Hawthorne effect

Question No. 18 Marks +1 -0 Time

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Which graphical representation is best suited for displaying the relationship between two quantitative variables?

A. Bar chart
B. Pie chart
C. Histogram
D. Scatter plot

Question No. 19 Marks +1 -0 Time

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In a probability experiment, the set of all possible outcomes is known as the:

A. Event space
B. Sample space
C. Outcome set
D. Possibility space

Question No. 20 Marks +1 -0 Time

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Evaluate the correctness of the following statements regarding sampling errors:

Pair 1: Sampling error can be reduced by increasing the sample size.
Pair 2: Non-sampling error is exclusively due to random chance.
Pair 3: A poorly designed questionnaire is a source of non-sampling error.
Pair 4: Sampling bias is a type of non-sampling error.

How many of the above pairs are correct?

A. 1
B. 2
C. 3
D. 4

Question No. 21 Marks +1 -0 Time

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What is the primary purpose of calculating the interquartile range (IQR)?

A. To determine the average value of a dataset.
B. To measure the spread of the middle 50% of the data.
C. To identify the most frequent value in a dataset.
D. To assess the overall range from minimum to maximum.

Question No. 22 Marks +1 -0 Time

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If P(A) = 0.4 and P(B) = 0.7, and A and B are independent events, what is P(A and B)?

A. 0.28
B. 0.11
C. 0.70
D. 0.40

Question No. 23 Marks +1 -0 Time

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Which non-probability sampling method relies on the researcher's judgment to select sample members who are considered most representative of the population or who possess specific characteristics?

A. Convenience sampling
B. Snowball sampling
C. Quota sampling
D. Purposive sampling

Question No. 24 Marks +1 -0 Time

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Consider the general steps involved in presenting data effectively, from raw collection to final visualization.

Data cleaning and organization.
Selection of appropriate graphical or tabular representation.
Data collection.
Interpretation and labeling of the visualization.

Which of the following sequences represents a logical flow?

A. 3, 1, 2, 4
B. 1, 3, 2, 4
C. 3, 2, 1, 4
D. 2, 1, 3, 4

Question No. 25 Marks +1 -0 Time

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If two events A and B are such that P(A) = 0.3, P(B) = 0.4, and P(A ∩ B) = 0, what does this imply about A and B?

A. They are independent.
B. They are mutually exclusive.
C. They are dependent but not mutually exclusive.
D. They are complementary.

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