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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

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

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
P0
Price in
2005
P1
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, ∑fi = 40
∑fidi = 35
By Assumed mean method,
Mean = a + (∑fidi/∑fi)
= 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
(fi)
Class
mark
(xi)mark
(xi)
di di =
xi – a= xi –
a
ffidi
30.5 – 35.5 9 33 -10 -90
35.5 – 40.5 6 38 -5 -25
40.5 – 45.5 15 43 = a 0 0
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 ∑fi = 40 ∑fidi = 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
(frequenc
y)
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!