Here are 25 multiple-choice questions on the Fundamentals of Statistics (including Probability), tailored for the JKSSB Forester Exam and similar competitive exams.
Fundamentals of Statistics (including Probability) – Multiple Choice Questions
Q1. Which branch of mathematics deals with the collection, analysis, interpretation, presentation, and organization of data?
(a) Algebra
(b) Calculus
(c) Statistics
(d) Geometry
Answer: (c)
Explanation: Statistics is the distinct branch of mathematics focused on all aspects of data handling, from collection to interpretation.
Q2. The raw material of statistics is generally referred to as:
(a) Information
(b) Facts
(c) Data
(d) Records
Answer: (c)
Explanation: Data refers to the unprocessed facts and figures from which conclusions can be drawn.
Q3. Which of the following is NOT a measure of central tendency?
(a) Mean
(b) Median
(c) Mode
(d) Range
Answer: (d)
Explanation: Mean, Median, and Mode are measures of central tendency, indicating the typical or central value of a dataset. Range is a measure of dispersion.
Q4. The sum of all observations divided by the total number of observations is known as the:
(a) Median
(b) Mode
(c) Mean
(d) Standard Deviation
Answer: (c)
Explanation: This is the definition of the arithmetic mean, often simply called the “mean.”
Q5. In a dataset arranged in ascending or descending order, the middle value is called the:
(a) Mean
(b) Median
(c) Mode
(d) Quartile
Answer: (b)
Explanation: The median is the middle value when the data is ordered. If there are two middle values (for an even number of observations), it’s their average.
Q6. The value that appears most frequently in a dataset is known as the:
(a) Mean
(b) Median
(c) Mode
(d) Average
Answer: (c)
Explanation: The mode is the observation with the highest frequency. A dataset can have no mode, one mode (unimodal), or multiple modes (multimodal).
Q7. For the dataset: 2, 5, 8, 2, 9, 5, 2, 11, what is the mode?
(a) 5
(b) 2
(c) 8
(d) 9
Answer: (b)
Explanation: The number 2 appears 3 times, which is more than any other number in the dataset.
Q8. For the dataset: 10, 12, 15, 18, 20, what is the median?
(a) 10
(b) 12
(c) 15
(d) 18
Answer: (c)
Explanation: The data is already ordered. There are 5 observations, so the middle value is the 3rd observation, which is 15.
Q9. If the mean of five observations is 10, and four of the observations are 8, 12, 9, 11, what is the fifth observation?
(a) 9
(b) 10
(c) 11
(d) 12
Answer: (b)
Explanation: Sum of observations = Mean × Number of observations = 10 × 5 = 50.
Sum of known observations = 8 + 12 + 9 + 11 = 40.
Fifth observation = Total Sum – Sum of known observations = 50 – 40 = 10.
Q10. Probability deals with the chance of an event occurring, expressed as a number between:
(a) -1 and 1
(b) 0 and 1
(c) 0 and 100
(d) -100 and 100
Answer: (b)
Explanation: Probability is always a value between 0 (impossible event) and 1 (certain event), inclusive.
Q11. What is the probability of rolling an even number on a standard six-sided die?
(a) 1/6
(b) 1/3
(c) 1/2
(d) 2/3
Answer: (c)
Explanation: The even numbers on a standard die are 2, 4, 6 (3 outcomes). The total possible outcomes are 1, 2, 3, 4, 5, 6 (6 outcomes). So, Probability = Favorable Outcomes / Total Outcomes = 3/6 = 1/2.
Q12. If a bag contains 3 red balls and 7 blue balls, what is the probability of drawing a red ball randomly?
(a) 3/10
(b) 7/10
(c) 3/7
(d) 1/3
Answer: (a)
Explanation: Total number of balls = 3 (red) + 7 (blue) = 10.
Number of favorable outcomes (red balls) = 3.
Probability (Red Ball) = 3/10.
Q13. An event that is impossible to occur has a probability of:
(a) 1
(b) 0.5
(c) 0
(d) -1
Answer: (c)
Explanation: An impossible event has a 0% chance of happening, so its probability is 0.
Q14. An event that is certain to occur has a probability of:
(a) 0
(b) 0.5
(c) 1
(d) 100
Answer: (c)
Explanation: A certain event has a 100% chance of happening, so its probability is 1.
Q15. The sum of the probabilities of all possible elementary outcomes of an experiment is always:
(a) Less than 1
(b) Equal to 1
(c) Greater than 1
(d) Dependent on the experiment
Answer: (b)
Explanation: The set of all possible outcomes is called the sample space, and the sum of probabilities of all individual outcomes in the sample space must equal 1.
Q16. What is the probability of drawing a ‘King’ from a well-shuffled deck of 52 playing cards?
(a) 1/52
(b) 1/13
(c) 4/13
(d) 1/4
Answer: (b)
Explanation: There are 4 Kings in a deck of 52 cards. Probability = 4/52 = 1/13.
Q17. The difference between the highest and lowest values in a dataset is called the:
(a) Mean Deviation
(b) Standard Deviation
(c) Range
(d) Variance
Answer: (c)
Explanation: Range is the simplest measure of dispersion and is calculated by subtracting the minimum value from the maximum value.
Q18. Which of the following is a disadvantage of the mode?
(a) It is affected by extreme values.
(b) It can be difficult to calculate for continuous data.
(c) It may not exist or be unique.
(d) It does not represent discrete data well.
Answer: (c)
Explanation: A dataset might have no values repeating (no mode) or multiple values repeating with the same highest frequency (multiple modes), making it less suitable in some cases.
Q19. Which measure of central tendency is most appropriate for a skewed distribution with outliers?
(a) Mean
(b) Median
(c) Mode
(d) Range
Answer: (b)
Explanation: The median is less affected by extreme values (outliers) and skewness compared to the mean, making it a better representative for such distributions.
Q20. If P(A) is the probability of event A occurring, then the probability of event A NOT occurring, P(not A), is given by:
(a) 1 + P(A)
(b) 1 – P(A)
(c) P(A) – 1
(d) 1 / P(A)
Answer: (b)
Explanation: The sum of the probability of an event occurring and the probability of it not occurring is always 1. So, P(not A) = 1 – P(A).
Q21. A coin is tossed twice. What is the probability of getting exactly one head?
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1
Answer: (b)
Explanation: Possible outcomes are: HH, HT, TH, TT. Favorable outcomes (exactly one head): HT, TH. Probability = 2/4 = 1/2.
Q22. In statistics, a numerical value that describes a characteristic of a sample is called a:
(a) Parameter
(b) Statistic
(c) Population
(d) Variable
Answer: (b)
Explanation: A statistic is a characteristic of a sample. A parameter is a characteristic of a population.
Q23. Which of the following is an example of primary data?
(a) Data collected from a government census report.
(b) Data from a research paper already published.
(c) Data collected through a direct survey by the researcher for a specific purpose.
(d) Data from a newspaper article.
Answer: (c)
Explanation: Primary data is original data collected firsthand by the researcher for their specific study. Other options are examples of secondary data.
Q24. The probability of getting a sum of 7 when rolling two standard six-sided dice is:
(a) 1/36
(b) 1/12
(c) 1/6
(d) 1/3
Answer: (c)
Explanation: Total possible outcomes when rolling two dice = 6 * 6 = 36.
Combinations that sum to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) – which are 6 favorable outcomes.
Probability = 6/36 = 1/6.
Q25. If a dataset has two modes, it is called:
(a) Unimodal
(b) Bimodal
(c) Trimodal
(d) Multimodal
Answer: (b)
Explanation: A dataset with one mode is unimodal, two modes is bimodal, and more than two modes is multimodal.
