1. What is the mean of the following data set: 5, 10, 15, 20, 25?
A) 10
B) 15
C) 20
D) 25
Answer: B
2. Which measure of central tendency is most affected by extreme values?
A) Mean
B) Median
C) Mode
D) Range
Answer: A
3. What does a standard deviation measure?
A) Central tendency
B) Variability
C) Correlation
D) Probability
Answer: B
4. If a data set has a mean of 50 and a standard deviation of 5, what is the z-score of a value 60?
A) 1
B) 2
C) 3
D) 4
Answer: B
5. What type of data can be classified into categories without any numerical value?
A) Continuous data
B) Discrete data
C) Nominal data
D) Ordinal data
Answer: C
6. In a normal distribution, what percentage of data falls within one standard deviation from the mean?
A) 50%
B) 68%
C) 95%
D) 99%
Answer: B
7. Which of the following is a measure of dispersion?
A) Median
B) Mode
C) Variance
D) Mean
Answer: C
8. If the correlation coefficient between two variables is -0.8, what does this indicate?
A) Strong positive relationship
B) Strong negative relationship
C) Weak positive relationship
D) No relationship
Answer: B
9. What is the mode of the following data set: 1, 2, 2, 3, 4, 5?
A) 1
B) 2
C) 3
D) 4
Answer: B
10. What type of sampling involves dividing a population into subgroups and then taking a random sample from each subgroup?
A) Simple random sampling
B) Stratified sampling
C) Systematic sampling
D) Cluster sampling
Answer: B
11. The sum of the probabilities of all possible outcomes of a random experiment is:
A) 0
B) 0.5
C) 1
D) Undefined
Answer: C
12. Which of the following distributions is symmetric?
A) Normal distribution
B) Exponential distribution
C) Poisson distribution
D) Binomial distribution
Answer: A
13. A Type I error occurs when:
A) A false null hypothesis is not rejected
B) A true null hypothesis is rejected
C) A false null hypothesis is rejected
D) A true alternative hypothesis is not accepted
Answer: B
14. What is the purpose of hypothesis testing?
A) To prove a hypothesis
B) To determine the validity of a hypothesis
C) To collect data
D) To describe a population
Answer: B
15. Which of the following is a non-parametric test?
A) t-test
B) ANOVA
C) Mann-Whitney U test
D) Z-test
Answer: C
16. In which of the following scenarios would you use a chi-square test?
A) To compare means
B) To assess the relationship between two categorical variables
C) To measure correlation
D) To test for normality
Answer: B
17. What is the primary assumption of the linear regression model?
A) The relationship between the variables is quadratic
B) The variables are independent
C) There is a linear relationship between the independent and dependent variables
D) The residuals are not normally distributed
Answer: C
18. If two events A and B are independent, what is the probability of both events occurring?
A) P(A) + P(B)
B) P(A) × P(B)
C) P(A) / P(B)
D) P(A) – P(B)
Answer: B
19. What does a p-value represent in hypothesis testing?
A) The probability of the null hypothesis being true
B) The probability of observing the test results under the null hypothesis
C) The significance level of the test
D) The probability of making a Type II error
Answer: B
20. A dataset has a mean of 20 and a median of 15. What can be inferred about the distribution?
A) It is symmetric
B) It is negatively skewed
C) It is positively skewed
D) There is not enough information
Answer: C
21. In a box plot, the line inside the box represents the:
A) Minimum value
B) Median
C) Mean
D) Maximum value
Answer: B
22. Which of the following is not a property of the normal distribution?
A) It is bell-shaped
B) It is symmetric
C) The mean, median, and mode are all equal
D) It has skewness of +1
Answer: D
23. What type of data is represented by the numbers 1, 2, 3, 4, and 5 in a ranking order?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
Answer: B
24. What is the variance of a dataset?
A) The square root of the standard deviation
B) The difference between the maximum and minimum values
C) The average of the squared deviations from the mean
D) The midpoint of the dataset
Answer: C
25. Which of the following is an example of a continuous random variable?
A) The number of students in a class
B) The height of students
C) The result of a dice roll
D) The gender of individuals
Answer: B
26. What does the Central Limit Theorem state?
A) The mean of the population is equal to the mean of the sample
B) The sum of a large number of independent random variables is normally distributed
C) The median is always equal to the mean
D) Probability distributions must be continuous
Answer: B
27. What is the 75th percentile of a data set?
A) The value below which 75% of the data falls
B) The value above which 75% of the data falls
C) The mean of the data set
D) The mode of the data set
Answer: A
28. If the correlation coefficient between two variables is close to 0, this indicates:
A) A strong positive relationship
B) A strong negative relationship
C) No linear relationship
D) A weak relationship
Answer: C
29. The interquartile range (IQR) is:
A) The difference between the highest and lowest values
B) The difference between the first and third quartiles
C) The average of the first and second quartiles
D) The median of the dataset
Answer: B
30. In a hypothesis test, the null hypothesis typically represents:
A) A statement of no effect or no difference
B) A statement of a significant effect
C) A theory that is yet to be tested
D) The result of the test
Answer: A
31. A data set with a positive skew will have:
A) A mean greater than the median
B) A mean less than the median
C) The mean equal to the median
D) No skewness
Answer: A
32. In statistics, a confidence interval is used to:
A) Measure variability
B) Estimate a population parameter
C) Conduct hypothesis testing
D) Create a visual representation of data
Answer: B
33. What is the primary goal of regression analysis?
A) To calculate the mean
B) To predict the value of a dependent variable based on independent variables
C) To compare two groups
D) To test a hypothesis
Answer: B
34. In a survey, if 40% of participants prefer product A, the 40% is known as:
A) Sample
B) Statistic
C) Parameter
D) Variable
Answer: B
35. The term “sample size” refers to:
A) The total population size
B) The number of observations in a sample
C) The average of the sample
D) The range of the sample
Answer: B
36. What is the main purpose of using a control group in experiments?
A) To test the hypothesis
B) To minimize bias
C) To provide a baseline for comparison
D) To increase sample size
Answer: C
37. Which of the following statements about the mean is true?
A) It is always an integer
B) It is sensitive to outliers
C) It cannot be calculated for categorical data
D) All of the above
Answer: B
38. A histogram displays:
A) Categorical data
B) Frequency distributions of numerical data
C) Percentages
D) Correlation coefficients
Answer: B
39. The probability of an event occurring is always between:
A) -1 and 1
B) 0 and 1
C) 0 and 100%
D) -100% and 100%
Answer: B
40. Which of the following describes a bimodal distribution?
A) One mode
B) Two modes
C) No mode
D) More than two modes
Answer: B
41. In statistical terms, the “null hypothesis” typically denotes:
A) The accepted theory
B) The theory that needs to be disproven
C) The average value of a population
D) The confidence level
Answer: B
42. A scatter plot is used to show the relationship between:
A) Two categorical variables
B) One categorical and one numerical variable
C) Two numerical variables
D) Three numerical variables
Answer: C
43. What is the purpose of using stratified sampling?
A) To reduce costs
B) To ensure all groups are represented
C) To simplify data collection
D) To increase sample size
Answer: B
44. The coefficient of determination (R²) indicates:
A) The strength of the relationship between two variables
B) The direction of the relationship
C) The total variance in the dependent variable
D) The percentage of variance explained by the independent variable
Answer: D
45. What does the term “outlier” refer to in statistics?
A) A value that falls within the normal range
B) A value that is significantly different from other observations
C) A value that is equal to the mean
D) A value that represents the median
Answer: B
46. Which of the following tests is used to compare means across three or more groups?
A) t-test
B) ANOVA
C) Chi-square test
D) Z-test
Answer: B
47. A sampling method that involves selecting every nth member of a population is known as:
A) Stratified sampling
B) Systematic sampling
C) Cluster sampling
D) Simple random sampling
Answer: B
48. The range of a dataset is:
A) The sum of all values
B) The average value
C) The difference between the maximum and minimum values
D) The median value
Answer: C
49. In statistics, the term “degrees of freedom” typically refers to:
A) The number of independent values in a calculation
B) The total number of observations
C) The sample size
D) The mean of the data
Answer: A
50. Which of the following is an example of a discrete random variable?
A) Temperature
B) Weight
C) Number of cars in a parking lot
D) Height
Answer: C
51. A sample is considered representative if:
A) It includes all members of the population
B) It is large enough
C) It accurately reflects the characteristics of the population
D) It is collected randomly
Answer: C
52. Which of the following is true about a standard normal distribution?
A) Mean is 0 and standard deviation is 1
B) Mean is 1 and standard deviation is 0
C) It is positively skewed
D) It has a mean greater than 1
Answer: A
53. What is a cumulative frequency distribution?
A) A summary of how often each value occurs
B) A total count of frequencies up to a certain value
C) A measure of central tendency
D) A comparison of different datasets
Answer: B
54. The concept of sampling error refers to:
A) The difference between the sample statistic and the actual population parameter
B) The error in measuring the sample
C) The cost of sampling
D) The time taken to collect samples
Answer: A
55. A random variable that can take on any value within a given range is called:
A) Discrete
B) Continuous
C) Nominal
D) Ordinal
Answer: B
56. Which of the following terms is used to describe the average of a squared deviation from the mean?
A) Variance
B) Standard deviation
C) Median
D) Mode
Answer: A
57. A p-value less than 0.05 typically indicates:
A) Strong evidence against the null hypothesis
B) Weak evidence against the null hypothesis
C) No evidence against the null hypothesis
D) The null hypothesis is true
Answer: A
58. What is the main goal of descriptive statistics?
A) To make predictions about a population
B) To summarize and organize data
C) To test hypotheses
D) To calculate probabilities
Answer: B
59. The probability of at least one success in n trials is equal to:
A) 1 – (1 – p)ⁿ
B) pⁿ
C) (1 – p)ⁿ
D) p + (1 – p)ⁿ
Answer: A
60. Which of the following indicates a weak positive correlation?
A) r = 0.9
B) r = 0.5
C) r = -0.2
D) r = 0.1
Answer: B
61. A probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials is known as:
A) Normal distribution
B) Binomial distribution
C) Poisson distribution
D) Exponential distribution
Answer: B
62. The process of estimating population parameters based on sample statistics is known as:
A) Sampling
B) Estimation
C) Data collection
D) Hypothesis testing
Answer: B
63. The term “population” in statistics refers to:
A) A sample taken from the larger group
B) The entire group of individuals or items
C) A subset of the sample
D) The mean of a dataset
Answer: B
64. Which of the following statistical tests is appropriate for comparing two independent samples?
A) Paired t-test
B) One-way ANOVA
C) Independent t-test
D) Chi-square test
Answer: C
65. What is the main difference between qualitative and quantitative data?
A) Qualitative data can be measured, while quantitative data cannot
B) Qualitative data is numerical, while quantitative data is categorical
C) Qualitative data describes qualities, while quantitative data represents numbers
D) There is no difference
Answer: C
66. What is a two-tailed test?
A) A test that assesses both extremes of the distribution
B) A test that only considers one side of the distribution
C) A test with a sample size of two
D) A test that measures the central tendency
Answer: A
67. A negatively skewed distribution will have:
A) A mean less than the median
B) A mean greater than the median
C) The mean equal to the mode
D) No skewness
Answer: A
68. In statistics, a “parameter” refers to:
A) A characteristic of a sample
B) A characteristic of a population
C) The average of a dataset
D) The median of a dataset
Answer: B
69. Which statistical measure would be best to describe a dataset with extreme outliers?
A) Mean
B) Median
C) Mode
D) Variance
Answer: B
70. A research study has a significance level (alpha) set at 0.01. What does this mean?
A) There is a 1% chance of making a Type II error
B) There is a 1% chance of making a Type I error
C) The power of the test is 1%
D) The sample size is too small
Answer: B
71. In a standard deviation, what does a higher value indicate?
A) Data points are clustered around the mean
B) Data points are widely spread out from the mean
C) All data points are identical
D) There is no variation in data
Answer: B
72. Which of the following is not a requirement for a normal distribution?
A) Symmetry
B) Mean equal to median
C) Bell-shaped
D) Defined range
Answer: D
73. The probability that an event will not occur is:
A) 1 minus the probability that it will occur
B) Always 0
C) Always 1
D) The same as the event occurring
Answer: A
74. If the z-score of a value is -2, what can be inferred about this value?
A) It is above the mean
B) It is below the mean
C) It is equal to the mean
D) It is an outlier
Answer: B
75. In a two-way ANOVA, the interaction effect examines:
A) The main effects of each independent variable
B) The combined effects of two independent variables on the dependent variable
C) The variability within groups
D) The differences in means across multiple groups
Answer: B
76. What does the term “sampling distribution” refer to?
A) The distribution of sample statistics obtained from repeated sampling
B) The distribution of population parameters
C) The frequency distribution of a single sample
D) The mean of all possible samples
Answer: A
77. The central limit theorem states that:
A) The means of larger samples are normally distributed regardless of the population distribution
B) All samples must be normally distributed
C) The median is always the best measure of central tendency
D) Outliers do not affect the mean
Answer: A
78. Which of the following is a characteristic of the Poisson distribution?
A) It describes continuous data
B) It is used for counting events in a fixed interval
C) It has a defined maximum value
D) It is always normally distributed
Answer: B
79. In hypothesis testing, a Type II error occurs when:
A) The null hypothesis is incorrectly rejected
B) The null hypothesis is incorrectly accepted
C) The sample size is too small
D) The significance level is too high
Answer: B
80. Which of the following graphs is commonly used to show the distribution of data?
A) Bar graph
B) Histogram
C) Pie chart
D) Line graph
Answer: B
81. Which is the capital city of Pakistan?
A) Lahore
B) Islamabad
C) Karachi
D) Quetta
Answer: B
82. The current President of Pakistan (as of 2024) is:
A) Imran Khan
B) Arif Alvi
C) Shehbaz Sharif
D) Bilawal Bhutto Zardari
Answer: B
83. What is the chemical symbol for water?
A) H₂O
B) O₂
C) CO₂
D) H₂
Answer: A
84. In which year did Pakistan gain independence?
A) 1945
B) 1947
C) 1950
D) 1955
Answer: B
85. The square root of 64 is:
A) 6
B) 8
C) 10
D) 12
Answer: B
86. Which of the following is a primary color?
A) Green
B) Yellow
C) Blue
D) Purple
Answer: C
87. The national language of Pakistan is:
A) Punjabi
B) English
C) Urdu
D) Sindhi
Answer: C
88. What is the capital of the United States?
A) New York
B) Washington, D.C.
C) Los Angeles
D) Chicago
Answer: B
89. The currency used in Pakistan is called:
A) Dollar
B) Rupee
C) Taka
D) Dirham
Answer: B
90. In which year did the Pakistan Movement begin?
A) 1930
B) 1940
C) 1947
D) 1950
Answer: B
91. What is the main function of the heart in the human body?
A) To digest food
B) To pump blood
C) To filter waste
D) To control breathing
Answer: B
92. What is the antonym of ‘difficult’?
A) Easy
B) Hard
C) Tough
D) Challenging
Answer: A
93. The largest continent in the world is:
A) Africa
B) Europe
C) Asia
D) Antarctica
Answer: C
94. In computer terminology, what does CPU stand for?
A) Central Programming Unit
B) Central Processing Unit
C) Central Peripheral Unit
D) Central Power Unit
Answer: B
95. What is the formula for calculating the area of a rectangle?
A) Length + Width
B) Length × Width
C) Length ÷ Width
D) 2 × (Length + Width)
Answer: B
96. Which of the following is NOT a programming language?
A) Python
B) Java
C) HTML
D) Microsoft
Answer: D
97. The poet of the national anthem of Pakistan is:
A) Allama Iqbal
B) Faiz Ahmed Faiz
C) Hafeez Jullundhri
D) Ahmad Faraz
Answer: C
98. Which planet is known as the “Red Planet”?
A) Venus
B) Mars
C) Jupiter
D) Saturn
Answer: B
99. The process of converting a solid directly into a gas is known as:
A) Evaporation
B) Condensation
C) Sublimation
D) Melting
Answer: C
100. The English word ‘happy’ is translated to Urdu as:
A) غمگین (Ghamgeen)
B) خوش (Khush)
C) خوفناک (Khofnak)
D) مایوس (Mayous)
Answer: B