Statistics question and answers with mcqs

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1. INDEX MCQ FILL IN THE BLANKS TRUE/FALSE SHORT ANSWER QUESTIONS NUMERICALS MIXED TYPE QUESTIONS

2. Question 1: What is the mean of the following numbers: 5, 10, 15, 20? A) 10 B) 12.5 C) 15 D) 17.5 Answer: B) 12.5

3. Question 2: What is the mode of the following set of numbers: 3, 5, 5, 7, 9, 9, 9, 11? A) 5 B) 7 C) 9 D) 11 Answer: C) 9

4. Question 3: Which measure of central tendency is most affected by outliers? A) Mean B) Median C) Mode D) Range Answer: A) Mean

5. Question 4: In a box plot, which part of the box represents the interquartile range? A) The whiskers B) The top of the box C) The bottom of the box D) The middle 50% of the box Answer: D) The middle 50% of the box

6. Question 5: What does the standard deviation measure in a dataset? A) Average value B) Spread or variability C) Median D) Mode Answer: B) Spread or variability

7. Question 6: If the correlation coefficient between two variables is -0.8, what type of relationship do they have? A) Strong positive B) Strong negative C) No relationship D) Weak positive Answer: B) Strong negative

8. Question 7: The bell-shaped curve used in statistics to represent the distribution of a dataset is known as: A) Pareto chart B) Pie chart C) Bar chart D) Normal distribution Answer: D) Normal distribution

9. Question 8: What is the range of a dataset? A) The difference between the smallest and largest values in the dataset B) The sum of all values in the dataset C) The most frequently occurring value in the dataset D) The average of all values in the dataset Answer: A) The difference between the smallest and largest values in the dataset

10. Question 9: Which of the following is a measure of the spread or variability of a dataset? A) Mean B) Median C) Mode D) Variance Answer: D) Variance

11. Question 10: In statistics, what is the purpose of a hypothesis test? A) To describe the data B) To summarize the data C) To test a specific claim or hypothesis D) To display data in a visual format Answer: C) To test a specific claim or hypothesis

12. Question 11: What is the first step in the hypothesis testing process? A) Collect data B) Formulate a null hypothesis C) Perform a statistical test D) Draw a conclusion Answer: A) Collect data

13. Question 12: If the p-value in a hypothesis test is less than the significance level (alpha), what should you do? A) Reject the null hypothesis B) Fail to reject the null hypothesis C) Modify the data D) Calculate the z-score Answer: A) Reject the null hypothesis

14. Question 13: What is the formula for calculating the probability of an event in a discrete probability distribution? A) P(x) = (x - μ) / σ B) P(x) = (x - μ) / N C) P(x) = (x - μ) / (N * σ) D) P(x) = Number of favorable outcomes / Total number of outcomes

15. Question 14: In a normal distribution, what percentage of the data falls within one standard deviation of the mean? A) 25% B) 50% C) 68% D) 95% Answer: C) 68%

16. Question 15: Which of the following is not a measure of central tendency? A) Mean B) Median C) Mode D) Range Answer: D) Range

17. FILL IN THE BANKS

18. 1.The range of a dataset is calculated as the maximum value minus the………. ANSWER- MINIMUM VALUE

19. 2. In a normal distribution, approximately [68%] of the data falls within one________ of the mean. ANSWER- standard deviation

20. 3.The measure of central tendency that is most affected by outliers is the_____. ANSWER-mean

21. 4. The formula for calculating the probability of an event in a discrete probability distribution is P(x) = Number of favorable outcomes /________ ANSWER- Total number of outcomes

22. 5. In statistics, what is the purpose of a hypothesis [In statistics, what is the purpose of a hypothesis_____ ANSWER-TEST

23. 6. The first step in the hypothesis testing process is to_____ ANSWER-COLLECT DATA

24. 7.The mode is the most frequently occurring value in a dataset. TRUE/FLASE. ANSWER-FALSE

25. 8. The bell-shaped curve used in statistics to represent the distribution of a dataset is known as the______ ANSWER-normal distribution

26. 9. The mean of a dataset is calculated as the sum of all values divided by the______ ANSWER-sample size

27. 10. In a box plot, the interquartile range is represented by the ________ of the box. ANSWER- middle 50%

28. 11 . A dataset with low variability has a small_________ ANSWER- standard deviation

29. 12. The middle value in a dataset when the data is arranged in ascending order is the______ ANSWER- median

30. 13. The measure of central tendency that may not exist or be unique in a dataset is the _______ ANSWER-MODE

31. 14. The probability of an event always falls between_________inclusive . ANSWER-0,1

32. 15. A random variable that can take any real value within a certain range is called a_________ ANSWER- continuous random variable

33. TRUE / FALSE

34. 1. True or False: The mode is the most frequently occurring value in a dataset. Answer: True

35. 2. True or False: In a normal distribution, approximately 95% of the data falls within one standard deviation of the mean Answer: False

36. 3. True or False: The range of a dataset is calculated as the difference between the largest and smallest values. Answer: True

37. 4. True or False: The median is not affected by extreme outliers in a dataset. Answer: True

38. 5. True or False: The bell-shaped curve used to represent the distribution of a dataset is known as the exponential distribution. Answer: False

39. 6. True or False: In a hypothesis test, the null hypothesis is typically a statement of no effect or no difference. Answer: True

40. 7. True or False: A p-value is a measure of the strength of evidence against the null hypothesis. Answer: True

41. 8. True or False: The interquartile range (IQR) represents the middle 50% of the data in a dataset. Answer: True

42. 9. True or False: The mean is the most appropriate measure of central tendency for data that follows a skewed distribution . Answer: False

43. 10. True or False: A z-score measures how many standard deviations a data point is from the mean. Answer: True

44. 11. True or False: The coefficient of determination (R-squared) measures the strength and direction of a linear relationship between two variables. Answer: True

45. 12. True or False: A histogram is a graphical representation of categorical data. Answer: False

46. 13. True or False: A confidence interval is a range of values that provides an estimate of a population parameter. Answer: True

47. 14. True or False: In a chi-square test, the null hypothesis assumes independence between two categorical variables. Answer: True

48. 15.True or False: Correlation implies causation, meaning that a strong correlation between two variables always indicates a cause-and-effect relationship. Answer: False

49. PART- B Question 1: The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base. Items Price in 1980 Price in 2005 Food 100 200 Clothing 20 25 Fuel and Lighting 15 20 House rent 30 40 Misc. 35 65

50. ANSWER: Items Price in 1980   P Price in 2005  P 1 Weight   W RW Food 100 200 75 15,000 Clothing 20 25 10 1,250 Fuel and Lighting 15 20 5 666.65 House Rent 30 40 6 799.98 Misc. 35 65 4 742.84        

51. QUESTION-2: Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y).                                                   

52. ANSWER:

53. Question 3. The size of land holdings of 380 families in a village is given below. Find the median size of land holdings .                               ANSWER:

54. So, the median class = Size of  (N/2) th item = 190 item 190th lies in the 129th cumulative frequency and the corresponding class interval is 200-300.                Median size of land holdings = 241.22 acres

55. Question 4. Calculate the Mean Deviation using Mean and Standard Deviation for the following distribution.

56. Answer:

57. Question 5. What is a variable? Distinguish between a discrete and a continuous variable. Answer: A measurable characteristic which takes different values at different points of time and in different circumstance is called a variable as it keeps varying. Different varibles vary differently and depending on the way they vary, they are broadly classified into two types S.N. Discrete Variable Continuous Variable (i) A discrete variable can take only whole numbers. A continuous variable can take any numerical value. (ii) Discrete varibles increase in finite jumps from one value to another and cannot take any intermediate value between them. Continuous variables can take any conceivable value and can be broken into infinite gradations. (iii) Examples-number of workers in a factory, number of residents in a colony, etc. Examples-height, weight, distance, etc.

58. Question 7. Interpret the values of r as 1, -1 and 0. Answer: If r = 0 the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence the variables may not be independent.  If r= 1 the correlation is perfectly positive. The relation between them is exact in the sense that if one increases, the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion. If r = -1 the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion. PART- C

59. QUESTION.8 Consider the following frequency distribution. Calculate the mean weight of students. Weight (in kg) 31-35 36 – 40 41 – 45 46 – 50 51 – 55 56 – 60 61 – 65 66 – 70 71 – 75 Number of Students 9 6 15 3 1 2 2 1 1 Here, ∑f i  = 40 ∑ f i d i  = 35 By Assumed mean method, Mean = a + (∑ f i d i /∑f i ) = 43 + (35/40) = 43 + 0.875 = 43.875 Therefore, the mean weight of the students is 43.875 kg

60. Class intervals Number of students (f i ) Class mark (x i ) mark (x i ) d i   d i  = x i  – a = x i  – a f f i d i 30.5 – 35.5 9 33 -10 -90 35.5 – 40.5 6 38 -5 -25 40.5 – 45.5 15 43 = a 45.5 – 50.5 3 48 5 15 50.5 – 55.5 1 53 10 10 55.5 – 60.5 2 58 15 30 60.5 – 65.5 2 63 20 40 65.5 – 70.5 1 68 25 25 70.5 – 75.5 1 73 30 30 Total ∑f i  = 40 ∑ f idi  = 35

61.   Marks 10-20 20-30 30-40 40-50 50 – 60 60-70 70 – 80 Number of Students 7 10 10 20 20 15 8 QUESTION.9 Calculate the median marks of students from the following distribution.

62. Class interval Number of students (frequency ) Cumulative frequency 10 – 20 7 7 20 – 30 10 17 30 – 40 10 27 = cf 40 – 50 20 = f 47 50 – 60 20 67 60 – 70 15 82 70 – 80 8 90 N/2 = 90/2 = 45 Cumulative frequency greater and nearer to 45 is 47, which lies in the interval 40 – 50 Median class is 40 – 50. Lower limit of the median class = l = 40 Class size = h = 10 Frequency of the median class = f = 20 Cumulative frequency of the class preceding the median class = c.f = 27 As we know, median= l + (n/2-c.f)*h/f Median = 40 + [(45 – 27)/20] × 10 = 40 + (18/2) = 40 + 9 = 49 Hence, the median marks of the students = 49.

63. THANK YOU!