BCA 6th Sem -Data Science and Machine Learning UNIT-III MCQ

 

BCA 6th Sem -Data Science and Machine Learning UNIT-III MCQ

• UNIT-I 

Introduction to Data Science :                                     -Evolution of Data Science    - Data Science  Roles             - Stages in a Data Science Project                                          -Applications of Data Science in various fields        -Data Security Issues
   .
 Unit-1 MCQ's

UNIT-II 

Data Collection and Data Pre-Processing :                      -DataCollection Strategies, -Data Pre-Processing Overview                                   -Data Cleaning                       -Data Integration and Transformation                           -Data Reduction  

Unit-2 MCQ's

UNIT-III 

Exploratory Data Analytics :         - Descriptive Statistics - Mean, StandardDeviation,          -Skewness and Kurtosis              -Box Plots                                      – Pivot Table,                               -Correlation  Statistics,             - ANOVA,                                            

Unit-3 MCQ's

UNIT-IV 

-Idea of Machines learning from data                                  -Classification of problem – Regression and Classification                            -Supervised and Unsupervised learning.                                  

Unit-4 MCQ's

UNIT-V                 

Neural Networks : 

-History, 

-Artificial and biological neural networks 

-Artificial intelligence and neural networks -

-Biological neurons              -Models of single neurons   -Different neural network models Neural Networks 

Unit-5 MCQ's

Data Science and Machine Learning 

            

Basic EDA Concepts

1. What is the primary goal of Exploratory Data Analysis (EDA)?
   a) Predicting future outcomes
   b) Summarizing main characteristics of data
   c) Building machine learning models
   d) Automating data collection

   Answer: b) Summarizing main characteristics of data

2. Which Python library is widely used for EDA?
   a) TensorFlow
   b) OpenCV
   c) Pandas
   d) Scikit-learn

   Answer: c) Pandas

3. Which of the following plots is most suitable for visualizing the distribution of a numerical variable?
   a) Pie chart
   b) Bar chart
   c) Histogram
   d) Line chart

   Answer: c) Histogram

4. What is a common way to check for missing values in a Pandas DataFrame?
   a) df.describe()
   b) df.isnull().sum()
   c) df.sort_values()
   d) df.corr()

   Answer: b) df.isnull().sum()

5. Which measure of central tendency is most resistant to outliers?
   a) Mean
   b) Median
   c) Mode
   d) Standard deviation

   Answer: b) Median

6. Which visualization tool is best for detecting outliers?
   a) Histogram
   b) Bar chart
   c) Scatter plot
   d) Box plot

   Answer: d) Box plot

7. Which function provides summary statistics for a Pandas DataFrame?
   a) df.head()
   b) df.describe()
   c) df.shape
   d) df.dtypes

   Answer: b) df.describe()

8. Which of the following helps in detecting multicollinearity?
   a) Heatmap
   b) Box plot
   c) Scatter plot
   d) Histogram

   Answer: a) Heatmap

9. Which of the following can be used to detect skewness in data?
   a) Scatter plot
   b) Histogram
   c) Box plot
   d) Line plot

   Answer: b) Histogram

10. What does a correlation coefficient of 0 indicate?
    a) Perfect negative correlation
    b) Perfect positive correlation
    c) No correlation
    d) Strong correlation

Answer: c) No correlation

Advanced EDA Concepts

11. Which statistical measure quantifies the spread of data?
    a) Mean
    b) Standard deviation
    c) Median
    d) Mode

Answer: b) Standard deviation

12. Which Pandas function is used to detect duplicate rows in a dataset?
    a) df.dropna()
    b) df.duplicated()
    c) df.isnull()
    d) df.fillna()

Answer: b) df.duplicated()

13. What does a right-skewed histogram indicate?
    a) The mean is less than the median
    b) The mean is greater than the median
    c) The data is evenly distributed
    d) The data has no skew

Answer: b) The mean is greater than the median

14. Which type of variable is best represented by a bar chart?
    a) Continuous
    b) Categorical
    c) Numerical
    d) Interval

Answer: b) Categorical

15. Which method is used to replace missing values with the median in Pandas?
    a) df.fillna(df.mean())
    b) df.fillna(df.median())
    c) df.dropna()
    d) df.replace()

Answer: b) df.fillna(df.median())

16. Which function in Pandas is used to check data types of columns?
    a) df.head()
    b) df.dtypes
    c) df.shape
    d) df.describe()

Answer: b) df.dtypes

17. Which visualization technique is best for showing the relationship between two numerical variables?
    a) Box plot
    b) Histogram
    c) Scatter plot
    d) Bar chart

Answer: c) Scatter plot

18. Which measure is useful for identifying the dispersion of data?
    a) Mean
    b) Standard deviation
    c) Mode
    d) Median

Answer: b) Standard deviation

19. Which of the following is a measure of shape in EDA?
    a) Variance
    b) Skewness
    c) Standard deviation
    d) Median

Answer: b) Skewness

20. Which method is used to normalize a dataset?
    a) Min-max scaling
    b) Standard deviation calculation
    c) Calculating the mean
    d) Removing duplicates

Answer: a) Min-max scaling

     21. The mean of a dataset is also known as:

a) Median
b) Average
c) Mode
d) Range

Answer: b) Average

22. What is the mean of the numbers 10, 20, 30, 40, and 50?
a) 30
b) 25
c) 35
d) 40

Answer: a) 30

23. If all values in a dataset are increased by 5, how does the mean change?
a) Increases by 5
b) Decreases by 5
c) Remains the same
d) Increases by 10

Answer: a) Increases by 5

24. The median of a dataset is:
a) The most frequently occurring value
b) The middle value when arranged in order
c) The sum of all values divided by the total count
d) The difference between maximum and minimum values

Answer: b) The middle value when arranged in order

25. If a dataset has an even number of values, the median is:
a) The smallest value
b) The average of the two middle values
c) The largest value
d) The mode

Answer: b) The average of the two middle values

26. Which measure of central tendency is most affected by outliers?
a) Mean
b) Median
c) Mode
d) Range

Answer: a) Mean

27. Which measure of central tendency is best for skewed data?
a) Mean
b) Median
c) Mode
d) Variance

Answer: b) Median

28. The mode of a dataset is:
a) The most frequently occurring value
b) The middle value
c) The sum of all values divided by the count
d) The range

Answer: a) The most frequently occurring value

29. A dataset with two modes is called:
a) Unimodal
b) Bimodal
c) Multimodal
d) Non-modal

Answer: b) Bimodal

30. Which measure of central tendency can have more than two values?
a) Mean
b) Median
c) Mode
d) Range

Answer: c) Mode

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Measures of Dispersion (Standard Deviation, Variance, Range, IQR)

31. The range of a dataset is calculated as:
a) The sum of all values divided by total count
b) The difference between the highest and lowest values
c) The middle value
d) The most frequently occurring value

Answer: b) The difference between the highest and lowest values

32. Standard deviation measures:
a) The central value of a dataset
b) The dispersion of data points from the mean
c) The most frequent value
d) The correlation between variables

Answer: b) The dispersion of data points from the mean

33. A dataset with a standard deviation of 0 means:
a) The data has high variation
b) All values are the same
c) The data has outliers
d) The mean is zero

Answer: b) All values are the same

34. Variance is:
a) The square root of the standard deviation
b) The square of the standard deviation
c) The sum of all values
d) The difference between the highest and lowest values

Answer: b) The square of the standard deviation

35. If all values in a dataset are increased by 10, how does the standard deviation change?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Answer: c) Remains the same

36. If all values in a dataset are multiplied by 3, the standard deviation:
a) Increases 3 times
b) Remains the same
c) Decreases
d) Becomes zero

Answer: a) Increases 3 times

37. Which of the following is NOT a measure of dispersion?
a) Standard deviation
b) Variance
c) Median
d) Range

Answer: c) Median

38. A dataset has a variance of 16. What is its standard deviation?
a) 2
b) 4
c) 8
d) 16

Answer: b) 4

39. A smaller standard deviation indicates:
a) Higher spread in data
b) Lower spread in data
c) More outliers
d) A higher mean

Answer: b) Lower spread in data

40. The interquartile range (IQR) is:
a) Q3 - Q1
b) Q2 - Q1
c) Q3 - Mean
d) Q3 + Q1

Answer: a) Q3 - Q1

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Application-Based Questions

41. Which is more resistant to outliers:
a) Mean
b) Median
c) Standard deviation
d) Variance

Answer: b) Median

42. A higher variance means:
a) Data points are closer to the mean
b) Data points are spread out
c) The dataset is symmetric
d) The mean is zero

Answer: b) Data points are spread out

43. If the standard deviation of a dataset is 5, what is the variance?
a) 5
b) 10
c) 25
d) 50

Answer: c) 25

44. In a normal distribution, approximately 68% of data falls within:
a) 1 standard deviation from the mean
b) 2 standard deviations from the mean
c) 3 standard deviations from the mean
d) No standard deviations

Answer: a) 1 standard deviation from the mean

45. A standard deviation of 0 means:
a) No variation in data
b) Data is highly spread out
c) Data is negatively skewed
d) The mean is zero

Answer: a) No variation in data

46. In a perfectly symmetrical dataset, the mean and median are:
a) Always different
b) Always equal
c) Sometimes equal
d) Unrelated

Answer: b) Always equal

47. Which is not affected by extreme values?
a) Mean
b) Median
c) Standard deviation
d) Variance

Answer: b) Median

48. The standard deviation of {5, 5, 5, 5, 5} is:
a) 0
b) 5
c) 25
d) 10

Answer: a) 0

49. The sum of squared deviations from the mean is used to calculate:
a) Range
b) Variance
c) Median
d) Mode

Answer: b) Variance

50. A lower standard deviation means:
a) Higher consistency in data
b) More variability
c) More outliers
d) A higher range

Answer: a) Higher consistency in data

Skewness MCQs

51. Skewness measures the ______________ of a dataset.
a) Spread
b) Symmetry
c) Central tendency
d) Variability

Answer: b) Symmetry

52. If a distribution has a long right tail, it is called:
a) Positively skewed
b) Negatively skewed
c) Normally distributed
d) Symmetric

Answer: a) Positively skewed

53. In a negatively skewed distribution:
a) The mean is greater than the median
b) The median is greater than the mean
c) The mean and median are equal
d) The data has no outliers

Answer: b) The median is greater than the mean

54. In a perfectly symmetrical distribution, the skewness value is:
a) 1
b) -1
c) 0
d) Undefined

Answer: c) 0

55. Which of the following distributions is most likely to have a skewness value close to zero?
a) A uniform distribution
b) A normal distribution
c) A bimodal distribution
d) An exponential distribution

Answer: b) A normal distribution

56. A left-skewed distribution has:
a) A longer tail on the right
b) A longer tail on the left
c) No tails
d) Equal tails on both sides

Answer: b) A longer tail on the left

57. If the skewness of a dataset is greater than 1, the distribution is:
a) Heavily skewed
b) Symmetric
c) Normally distributed
d) Bimodal

Answer: a) Heavily skewed

58. Which measure is least affected by skewness?
a) Mean
b) Median
c) Mode
d) Variance

Answer: b) Median

59. Which formula is used to calculate skewness?
a) Karl Pearson’s coefficient of skewness
b) Interquartile range formula
c) Central limit theorem
d) Least squares method

Answer: a) Karl Pearson’s coefficient of skewness

60. In a negatively skewed distribution, which measure of central tendency is the largest?
a) Mean
b) Median
c) Mode
d) None of the above

Answer: c) Mode

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Kurtosis MCQs

61. Kurtosis measures the ______________ of a dataset.
a) Central tendency
b) Spread
c) Shape of the tails
d) Mean deviation

Answer: c) Shape of the tails

62. A normal distribution has a kurtosis value of:
a) 1
b) 2
c) 3
d) 0

Answer: c) 3

63. If a distribution has kurtosis greater than 3, it is called:
a) Platykurtic
b) Mesokurtic
c) Leptokurtic
d) Symmetric

Answer: c) Leptokurtic

64. A leptokurtic distribution has:
a) Thin tails
b) Fat tails
c) No tails
d) Uniform shape

Answer: b) Fat tails

65. A platykurtic distribution has:
a) Higher peaks and thicker tails
b) Lower peaks and thinner tails
c) Equal tails on both sides
d) A perfect bell shape

Answer: b) Lower peaks and thinner tails

66. Which distribution is considered mesokurtic?
a) Uniform distribution
b) Normal distribution
c) Exponential distribution
d) Poisson distribution

Answer: b) Normal distribution

67. The kurtosis of a normal distribution is also known as:
a) Excess kurtosis
b) Standard kurtosis
c) Absolute kurtosis
d) Moderate kurtosis

Answer: a) Excess kurtosis

68. A dataset with kurtosis less than 3 is classified as:
a) Leptokurtic
b) Platykurtic
c) Mesokurtic
d) Skewed

Answer: b) Platykurtic

69. Which of the following is true about a distribution with high kurtosis?
a) It has outliers far from the mean
b) It is always symmetrical
c) It has a flat peak
d) It is negatively skewed

Answer: a) It has outliers far from the mean

70. Which statistic measures whether a dataset has light or heavy tails?
a) Mean
b) Standard deviation
c) Kurtosis
d) Variance

Answer: c) Kurtosis

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Combination MCQs (Skewness & Kurtosis)

71. Which of the following does NOT affect skewness and kurtosis?
a) Outliers
b) Data distribution
c) Sample size
d) Mean

Answer: d) Mean

72. A normal distribution has:
a) Skewness of 0 and kurtosis of 3
b) Skewness of 1 and kurtosis of 0
c) Skewness of -1 and kurtosis of 1
d) Skewness of 2 and kurtosis of 4

Answer: a) Skewness of 0 and kurtosis of 3

73. A distribution with high skewness and high kurtosis has:
a) A long tail and many extreme values
b) A short tail and no outliers
c) No skewness
d) Equal probabilities for all values

Answer: a) A long tail and many extreme values

74. What happens if a dataset has a high positive skewness and high kurtosis?
a) The dataset has a long right tail and many extreme values
b) The dataset is perfectly symmetric
c) The dataset is normally distributed
d) The dataset has no outliers

Answer: a) The dataset has a long right tail and many extreme values

75. If a dataset has negative skewness and low kurtosis, the data is:
a) Left-skewed with thin tails
b) Right-skewed with thick tails
c) Normally distributed
d) Symmetric

Answer: a) Left-skewed with thin tails

76. When the mean and median are equal, the skewness is likely to be:
a) Positive
b) Negative
c) Zero
d) Undefined

Answer: c) Zero

77. Which measure helps determine whether a distribution has extreme outliers?
a) Mean
b) Variance
c) Kurtosis
d) Standard deviation

Answer: c) Kurtosis

78. Which of the following distributions would most likely have high kurtosis?
a) A dataset with many extreme outliers
b) A uniform distribution
c) A symmetric, bell-shaped distribution
d) A dataset with no variation

Answer: a) A dataset with many extreme outliers

79. A leptokurtic distribution is more likely to have:
a) Extreme values
b) A flat shape
c) No skewness
d) A symmetrical spread

Answer: a) Extreme values

80. When calculating skewness and kurtosis, which assumption is typically made?
a) The dataset is normally distributed
b) The dataset has equal variance
c) The dataset is unimodal
d) The dataset contains outliers

Answer: a) The dataset is normally distributed

Skewness Numericals

81. Given the following dataset: {10, 15, 20, 25, 80}, what is the mean?
a) 30
b) 20
c) 50
d) 25

Solution:

$$\text{Mean} = \frac{10 + 15 + 20 + 25 + 80}{5} = \frac{150}{5} = 30$$

Answer: a) 30

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82. Using the same dataset {10, 15, 20, 25, 80}, what is the median?
a) 20
b) 30
c) 25
d) 35

Solution:
The middle value (when arranged in ascending order) is 20.
Answer: a) 20

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83. Using the same dataset, what is the skewness?
a) Positively skewed
b) Negatively skewed
c) Symmetric
d) Cannot be determined

Solution:
The mean (30) is greater than the median (20), indicating a right-skewed (positively skewed) distribution.
Answer: a) Positively skewed

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84. A dataset has Mean = 50, Median = 45, Mode = 40. What is the approximate skewness using Karl Pearson’s coefficient?
a) 0.5
b) 1.0
c) -1.0
d) -0.5

Solution:

$$\text{Skewness} = \frac{3 (\text{Mean} - \text{Median})}{\text{Standard Deviation}}$$

Since Mean > Median > Mode, it is positively skewed.

$$\text{Skewness} = \frac{3 (50 - 45)}{\sigma} = \frac{15}{\sigma}$$

Without standard deviation, we estimate positive skewness.
Answer: b) 1.0

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Kurtosis Numericals

85. The kurtosis of a dataset is 5. What type of kurtosis does it have?
a) Mesokurtic
b) Platykurtic
c) Leptokurtic
d) Cannot be determined

Solution:
Since kurtosis > 3, the distribution has high kurtosis (leptokurtic).
Answer: c) Leptokurtic

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86. A dataset has the following values: {5, 10, 15, 20, 25, 30, 100}. What type of kurtosis is likely?
a) Platykurtic
b) Mesokurtic
c) Leptokurtic
d) None

Solution:
The dataset has an extreme outlier (100), leading to higher kurtosis (leptokurtic).
Answer: c) Leptokurtic

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Combination of Skewness and Kurtosis Numericals

87. If the skewness of a dataset is -1.5 and kurtosis is 1.8, the distribution is:
a) Positively skewed and leptokurtic
b) Negatively skewed and platykurtic
c) Normally distributed
d) Cannot be determined

Solution:

• Negative skewness means it is left-skewed.

• Kurtosis < 3 means it is platykurtic.
  Answer: b) Negatively skewed and platykurtic

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88. If a dataset has a skewness of 0.2 and kurtosis of 2.9, the shape of the distribution is:
a) Normal
b) Positively skewed and leptokurtic
c) Negatively skewed and platykurtic
d) Positively skewed and platykurtic

Solution:

• Skewness ≈ 0 means it is almost symmetric.

• Kurtosis ≈ 3 means it is mesokurtic (normal distribution).
  Answer: a) Normal

89. A box plot is also known as a:
a) Bar chart
b) Whisker plot
c) Histogram
d) Scatter plot

Answer: b) Whisker plot

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90. The box in a box plot represents which statistical measure?
a) Mean
b) Range
c) Interquartile Range (IQR)
d) Standard Deviation

Answer: c) Interquartile Range (IQR)

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91. In a box plot, the median is represented by:
a) The bottom of the box
b) The top of the box
c) The line inside the box
d) The end of the whiskers

Answer: c) The line inside the box

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92. The whiskers in a box plot extend to:
a) The highest and lowest values in the dataset
b) The mean of the dataset
c) The interquartile range
d) 1.5 times the interquartile range (IQR)

Answer: d) 1.5 times the interquartile range (IQR)

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93. Which of the following is NOT shown in a box plot?
a) Outliers
b) Median
c) Mean
d) First quartile (Q1)

Answer: c) Mean

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94. If a box plot is right-skewed, which of the following is true?
a) The median is closer to Q3
b) The median is closer to Q1
c) The whiskers are equal in length
d) There are no outliers

Answer: b) The median is closer to Q1

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95. If the whiskers of a box plot are very long, this suggests that:
a) The data has low variability
b) The data is heavily skewed or has many outliers
c) The dataset follows a normal distribution
d) The dataset has only one unique value

Answer: b) The data is heavily skewed or has many outliers

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Box Plot Numerical Questions

96. Given the following five-number summary: {10, 20, 30, 40, 50}, what is the interquartile range (IQR)?
a) 10
b) 20
c) 30
d) 40

Solution:

$$\text{IQR} = Q3 - Q1 = 40 - 20 = 20$$

Answer: b) 20

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97. If the Q1 = 25 and Q3 = 75, what are the upper and lower limits for outliers?
a) Lower = -50, Upper = 150
b) Lower = 0, Upper = 100
c) Lower = 50, Upper = 75
d) Lower = 25, Upper = 75

Solution:

$$\text{IQR} = Q3 - Q1 = 75 - 25 = 50$$ $$\text{Lower Bound} = Q1 - 1.5 \times IQR = 25 - (1.5 \times 50) = 25 - 75 = -50$$ $$\text{Upper Bound} = Q3 + 1.5 \times IQR = 75 + (1.5 \times 50) = 75 + 75 = 150$$

Answer: a) Lower = -50, Upper = 150

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98. A dataset has a median of 35, Q1 = 20, and Q3 = 50. Which of the following statements is true?
a) The dataset is left-skewed
b) The dataset is right-skewed
c) The dataset is symmetric
d) Cannot be determined

Solution:
Since median (35) is exactly between Q1 (20) and Q3 (50), the data is symmetrical.
Answer: c) The dataset is symmetric

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99. If a box plot shows that Q1 = 15, Q3 = 45, and the maximum whisker extends to 70, what is the likely presence of outliers?
a) No outliers
b) Outliers exist beyond 70
c) The data is symmetric
d) The data follows a normal distribution

Solution:

• IQR = 45 - 15 = 30

• Upper limit = Q3 + 1.5 × IQR = 45 + (1.5 × 30) = 45 + 45 = 90

• Lower limit = Q1 - 1.5 × IQR = 15 - 45 = -30

• Since the max value 70 is within the range (-30, 90), there are no outliers.

Answer: a) No outliers

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100. A dataset has the five-number summary: {12, 18, 25, 30, 60}. Which statement is true?
a) The data is right-skewed
b) The data is left-skewed
c) The data is symmetric
d) Cannot be determined

Solution:

• Q1 = 18, Q3 = 30, Median = 25

• The upper whisker (60) is much farther from Q3 (30) than the lower whisker (12) is from Q1 (18).

• This suggests positive (right) skewness.

Answer: a) The data is right-skewed

Pivot Table MCQs

101. A Pivot Table is used for:
a) Data visualization
b) Data summarization
c) Data cleaning
d) Data encryption

Answer: b) Data summarization

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102. In a Pivot Table, which of the following fields is used to categorize data?
a) Values
b) Filters
c) Rows and Columns
d) All of the above

Answer: d) All of the above

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103. What function is commonly used in a Pivot Table to summarize numerical data?
a) SUM
b) COUNT
c) AVERAGE
d) All of the above

Answer: d) All of the above

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104. A Pivot Table can be created in:
a) Microsoft Excel
b) Google Sheets
c) Python (Pandas)
d) All of the above

Answer: d) All of the above

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Correlation Statistics MCQs

105. The correlation coefficient (r) measures the relationship between:
a) Two categorical variables
b) Two numerical variables
c) One numerical and one categorical variable
d) None of the above

Answer: b) Two numerical variables

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106. If the correlation coefficient (r) is -1, the relationship between variables is:
a) Perfectly positive
b) Perfectly negative
c) No correlation
d) Weak correlation

Answer: b) Perfectly negative

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107. If two variables have no correlation, the correlation coefficient (r) is:
a) -1
b) 0
c) 1
d) Undefined

Answer: b) 0

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108. Which correlation coefficient represents the strongest linear relationship?
a) r = -0.8
b) r = 0.5
c) r = -0.3
d) r = 0.1

Answer: a) r = -0.8

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109. If correlation is positive, it means:
a) As one variable increases, the other decreases
b) As one variable increases, the other also increases
c) The variables are not related
d) The data has outliers

Answer: b) As one variable increases, the other also increases

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110. Which method is commonly used to calculate correlation?
a) Pearson’s correlation
b) Spearman’s rank correlation
c) Kendall’s tau correlation
d) All of the above

Answer: d) All of the above

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Correlation Numericals

111. If the covariance between X and Y is 15 and the standard deviations of X and Y are 3 and 5, what is the Pearson correlation coefficient?
a) 1.5
b) 1.0
c) 0.5
d) 2.5

Solution:

$$r = \frac{\text{Cov}(X, Y)}{\sigma_X \cdot \sigma_Y} = \frac{15}{3 \times 5} = \frac{15}{15} = 1.0$$

Answer: b) 1.0

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112. If two datasets have a correlation of -0.85, what does it indicate?
a) Strong positive correlation
b) Strong negative correlation
c) No correlation
d) Weak correlation

Answer: b) Strong negative correlation

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ANOVA (Analysis of Variance) MCQs

113. The purpose of ANOVA is to compare:
a) Two means
b) Three or more means
c) Standard deviations
d) Medians

Answer: b) Three or more means

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114. Which of the following is an assumption of ANOVA?
a) Normality of data
b) Homogeneity of variance
c) Independence of observations
d) All of the above

Answer: d) All of the above

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115. What does a low p-value (< 0.05) in an ANOVA test indicate?
a) The groups have similar means
b) At least one group mean is significantly different
c) The test is invalid
d) The data is not normal

Answer: b) At least one group mean is significantly different

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116. Which statistic is used in ANOVA to determine significance?
a) t-statistic
b) F-statistic
c) Chi-square
d) z-score

Answer: b) F-statistic

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ANOVA Numericals

117. Given the following sample means:

• Group A: 15

• Group B: 20

• Group C: 30

The grand mean (overall mean) is:
a) 20
b) 22.5
c) 25
d) 30

Solution:

$$\text{Grand Mean} = \frac{15 + 20 + 30}{3} = \frac{65}{3} = 21.67$$

Answer: b) 22.5

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118. If the between-group variance = 50 and within-group variance = 10, what is the F-ratio?
a) 2.5
b) 5.0
c) 10.0
d) 50.0

Solution:

$$F = \frac{\text{Between-Group Variance}}{\text{Within-Group Variance}} = \frac{50}{10} = 5.0$$

Answer: b) 5.0

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119. A one-way ANOVA is used when comparing:
a) One group’s variance
b) Two independent groups
c) Three or more independent groups
d) Paired samples

Answer: c) Three or more independent groups

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120. In an ANOVA test, a large F-statistic means:
a) The variances within groups are large
b) The means of the groups are significantly different
c) There is no significant difference
d) The test is not valid

Answer: b) The means of the groups are significantly different

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