(A) Need for Statistics, Frequency Distribution, Graphs, Central Tendency, Variability
- Which of the following best describes the primary purpose of statistics in education?
A. To conduct interviews
B. To manipulate data
C. To organize, analyze and interpret educational data
D. To establish classroom rules
Answer: C - Frequency distribution is used to:
A. Measure the intelligence of students
B. Summarize data and show how often each score occurs
C. Calculate mean and median
D. Rank students according to height
Answer: B - A histogram is best used when data is:
A. Nominal
B. Ordinal
C. Continuous
D. Qualitative
Answer: C - Which of the following is not a measure of central tendency?
A. Mode
B. Median
C. Range
D. Mean
Answer: C - The sum of deviations of scores from the mean is always:
A. Zero
B. One
C. Minimum
D. Maximum
Answer: A - A frequency polygon is constructed using:
A. Bar heights
B. Curve of best fit
C. Midpoints of class intervals
D. Cumulative percentages
Answer: C - Which measure is most affected by extreme scores?
A. Median
B. Mode
C. Mean
D. Range
Answer: C - If all scores in a distribution are equal, the standard deviation is:
A. Zero
B. One
C. Maximum
D. Equal to the mean
Answer: A - The most stable measure of central tendency is:
A. Mode
B. Median
C. Mean
D. Range
Answer: C - Which of the following graphs is suitable for comparing parts of a whole?
A. Line graph
B. Pie chart
C. Bar diagram
D. Histogram
Answer: B - The variability that considers all the scores in the distribution is:
A. Range
B. Interquartile range
C. Mean deviation
D. Standard deviation
Answer: D - Which measure of variability is the simplest to compute?
A. Variance
B. Standard deviation
C. Range
D. Mean deviation
Answer: C - Cumulative frequency distribution helps in determining:
A. Mean
B. Mode
C. Percentiles
D. Standard deviation
Answer: C - In a positively skewed distribution, the relationship among mean, median and mode is:
A. Mean < Median < Mode
B. Mean > Median > Mode
C. Mode = Mean > Median
D. Mean = Mode = Median
Answer: B - Which measure of central tendency is appropriate for qualitative data?
A. Mean
B. Median
C. Mode
D. Range
Answer: C - Which graphical representation is best suited for frequency distribution?
A. Line chart
B. Histogram
C. Pie chart
D. Scatterplot
Answer: B - The interquartile range includes:
A. The entire data
B. Middle 50% of scores
C. Top 25%
D. Bottom 25%
Answer: B - A symmetrical distribution has:
A. Mean > Mode
B. Mean < Median
C. Mean = Median = Mode
D. Median > Mode
Answer: C - The sum of squares of deviations divided by number of observations gives:
A. Mean
B. Standard deviation
C. Variance
D. Mode
Answer: C - The graphical method for checking normality of a distribution is:
A. Histogram
B. Boxplot
C. Scatterplot
D. Q–Q Plot
Answer: D - Which of the following is a characteristic of a good measure of central tendency?
A. Difficult to compute
B. Based on partial data
C. Clearly defined and stable
D. Sensitive to extreme values only
Answer: C - Standard deviation is best described as:
A. A measure of correlation
B. A measure of central tendency
C. A measure of dispersion
D. A type of curve
Answer: C - A data set with low standard deviation implies that:
A. Scores are widely spread
B. Scores are highly variable
C. Scores are close to the mean
D. Distribution is skewed
Answer: C - If range is 40 and number of class intervals is 10, the class width is:
A. 4
B. 6
C. 5
D. 8
Answer: C - Which type of scale is used in bar graphs typically?
A. Ratio
B. Nominal
C. Ordinal
D. Interval
Answer: B
(B) Normal Curve, Skewness, Kurtosis, Percentile, Derived Scores, Correlation
- Which of the following graphs represents a normal distribution?
A. U-shaped curve
B. J-shaped curve
C. Bell-shaped curve
D. Exponential curve
Answer: C - In a normal distribution, approximately what percentage of scores lie within ±1 standard deviation from the mean?
A. 50%
B. 68%
C. 75%
D. 95%
Answer: B - Which of the following is a property of the normal probability curve?
A. It is skewed to the right
B. It is skewed to the left
C. It is asymmetrical
D. The mean, median, and mode are equal
Answer: D - A distribution with a longer tail to the right is said to be:
A. Symmetrical
B. Positively skewed
C. Negatively skewed
D. Mesokurtic
Answer: B - Kurtosis measures the:
A. Symmetry of distribution
B. Central tendency
C. Peakness or flatness of the distribution
D. Correlation between variables
Answer: C - A platykurtic distribution is:
A. More peaked than normal
B. Skewed left
C. Flatter than the normal curve
D. Perfectly symmetrical
Answer: C - A percentile rank of 80 means that the student scored:
A. Higher than 80 students
B. Below 80% of the scores
C. Better than 80% of the group
D. 80% correct answers
Answer: C - Which of the following derived scores has a mean of 100 and SD of 15?
A. T-score
B. Z-score
C. Standard score
D. IQ score
Answer: D - Which score has a mean of 50 and SD of 10?
A. IQ score
B. T-score
C. Z-score
D. Percentile rank
Answer: B - A Z-score of 0 indicates a score that is:
A. One standard deviation below the mean
B. Equal to the mean
C. Two SDs above the mean
D. Below average
Answer: B - Z-scores allow comparison of:
A. Only scores within one test
B. Raw scores from different distributions
C. Only IQ scores
D. Skewness and kurtosis
Answer: B - The coefficient of correlation measures:
A. Strength and direction of relationship between two variables
B. Central tendency
C. Variability
D. Symmetry of curve
Answer: A - Which correlation method is used for ranked data?
A. Point-biserial correlation
B. Product moment method
C. Spearman’s rank difference method
D. Phi coefficient
Answer: C - Pearson’s Product Moment Correlation is suitable when data is:
A. Ordinal
B. Nominal
C. Interval or Ratio
D. Categorical
Answer: C - A correlation coefficient of -0.85 indicates:
A. Strong positive correlation
B. Weak positive correlation
C. Strong negative correlation
D. No correlation
Answer: C - When correlation is zero, it means:
A. One variable increase as the other increases
B. There is no relationship
C. One variable affects the other
D. Variables are identical
Answer: B - The highest possible value of Pearson’s r is:
A. 1.5
B. 1
C. 0.5
D. ∞
Answer: B - When all points lie exactly on a straight line sloping upwards, the correlation coefficient is:
A. -1
B. 0
C. +1
D. +0.5
Answer: C - Negative correlation means that:
A. Both variables increase together
B. One increases as the other decreases
C. Variables are not related
D. Values are always positive
Answer: B - A percentile score of 25 means the student scored:
A. At the top 25%
B. Better than 25% of peers
C. Exactly at the mean
D. In the lowest quartile
Answer: B - The area under the normal curve is equal to:
A. 1
B. 100
C. 0
D. Cannot be determined
Answer: A - Standard scores help in:
A. Reducing test items
B. Interpreting raw scores
C. Increasing deviation
D. Calculating reliability
Answer: B - A perfectly normal distribution has a skewness value of:
A. 0
B. +1
C. -1
D. 3
Answer: A - The term ‘mesokurtic’ refers to:
A. Flat curve
B. Normal peakedness
C. Extremely peaked curve
D. Skewed distribution
Answer: B - A high standard deviation in test scores implies:
A. Students are performing similarly
B. Scores are tightly grouped
C. Wide variation in performance
D. Test is too easy
Answer: C
(B) Normal Curve, Percentile, Derived Scores, Correlation – Continued
- Which of the following best defines Percentile Rank?
A. Position of a score in the frequency distribution
B. Percentage of scores equal to a given score
C. Percentage of scores below a given score
D. Number of students who scored above average
Answer: C - Which of the following is a limitation of percentile ranks?
A. They show equal intervals between scores
B. They cannot be converted to z-scores
C. They are not equally spaced
D. They cannot be graphed
Answer: C - The formula for Pearson’s product moment correlation coefficient is based on:
A. Mean and standard deviation
B. Deviations from mode
C. Median differences
D. Score ranges
Answer: A - The correlation coefficient lies between:
A. -2 and +2
B. -1 and +1
C. 0 and 1
D. -0.5 and +0.5
Answer: B - If r = 0.00, it means:
A. Perfect positive relationship
B. Perfect negative relationship
C. No linear relationship
D. Moderate relationship
Answer: C - The closer the value of r is to ±1, the:
A. Weaker the relationship
B. Stronger the relationship
C. More random the data
D. More skewed the data
Answer: B - What is the main use of derived scores in education?
A. To replace raw scores with test names
B. To convert all tests into percentages
C. To compare student performance across different tests
D. To display scores in tabular format
Answer: C - Which of the following is a non-parametric correlation?
A. Pearson’s r
B. Point-biserial correlation
C. Spearman’s rank correlation
D. Partial correlation
Answer: C - Which score transformation standardizes scores by converting raw scores into standard deviation units?
A. T-score
B. IQ score
C. Z-score
D. Percentile rank
Answer: C - T-scores are used to avoid:
A. Negative values in Z-scores
B. Variance in raw scores
C. Flat distribution
D. Central tendency
Answer: A - Which of the following is not a graphical method of representing frequency distribution?
A. Bar chart
B. Frequency polygon
C. Histogram
D. Scatter diagram
Answer: D - Which statistical term refers to the square of the standard deviation?
A. Range
B. Mean
C. Variance
D. Skewness
Answer: C - Which of the following best describes the use of the normal curve in education?
A. For lesson planning
B. For measuring syllabus difficulty
C. For interpreting scores and standardization
D. For preparing exam time-tables
Answer: C - A perfectly symmetrical distribution has:
A. Skewness of 1
B. Kurtosis of 3
C. Mean = Median = Mode
D. All scores equal
Answer: C - Which of the following is a measure of relative position?
A. Mean
B. Standard deviation
C. Percentile rank
D. Range
Answer: C - The correlation method suitable when data are not normally distributed is:
A. Pearson r
B. Spearman’s rho
C. Product moment method
D. Linear regression
Answer: B - What does a correlation coefficient of +0.70 indicate?
A. No relationship
B. Strong positive relationship
C. Weak negative relationship
D. Complete inverse relationship
Answer: B - Which graphical representation is used to study correlation?
A. Histogram
B. Pie chart
C. Scatter plot
D. Frequency polygon
Answer: C - If two variables move in opposite directions, the correlation is:
A. Zero
B. Positive
C. Negative
D. Nonexistent
Answer: C - Which statistical term refers to how scores are spread out or clustered around the mean?
A. Central tendency
B. Variability
C. Correlation
D. Percentile
Answer: B - A standard deviation of zero means that all scores:
A. Are very high
B. Are very low
C. Are the same
D. Follow a normal curve
Answer: C - Which of the following is used to determine the percentile rank of a score?
A. Cumulative frequency distribution
B. Raw frequency
C. Bar chart
D. Scatter plot
Answer: A - A z-score of -2.0 means the score is:
A. 2 points below the mean
B. 2 standard deviations below the mean
C. The lowest score in the distribution
D. Below the median but above the mode
Answer: B - Which correlation technique assumes a linear relationship and normal distribution?
A. Spearman’s
B. Chi-square
C. Pearson’s
D. Tetrachoric
Answer: C - If a student’s T-score is 70, what does it indicate?
A. Average performance
B. Two standard deviations above the mean
C. Two standard deviations below the mean
D. One SD above the mean
Answer: B
(B) Continued — Normal Curve, Percentiles, Derived Scores, Correlation, Applications
- What does a high positive correlation between two variables suggest?
A. Both variables move in opposite directions
B. One variable affects the other directly
C. As one increases, the other increases
D. No relationship exists
Answer: C - Which of the following is a parametric test of correlation?
A. Spearman’s rank correlation
B. Pearson’s product moment correlation
C. Chi-square test
D. Kruskal–Wallis test
Answer: B - Which is the most appropriate graphical method for visualizing a bivariate relationship?
A. Histogram
B. Bar graph
C. Scatter plot
D. Pie chart
Answer: C - The area under the normal curve from -∞ to +∞ is:
A. 0
B. 1
C. 100
D. 50
Answer: B - Which of the following is true about z-scores?
A. They have a fixed range
B. They can be negative or positive
C. They are always greater than 1
D. They are used only for IQ tests
Answer: B - In a normal distribution, what percent of scores fall between ±2 SD from the mean?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: C - Which of the following best represents the characteristics of a skewed distribution?
A. Mean = Median = Mode
B. Tail is equal on both sides
C. One tail is longer than the other
D. Bell-shaped curve
Answer: C - Which measure is most suitable when data contains extreme scores?
A. Mean
B. Mode
C. Median
D. Range
Answer: C - Which of the following is a measure of correlation that is not affected by extreme scores?
A. Pearson’s r
B. Spearman’s rank correlation
C. Regression coefficient
D. Coefficient of determination
Answer: B - The standard deviation is calculated based on:
A. Deviations from the mode
B. Deviations from the mean
C. Deviations from the median
D. Average range
Answer: B - When is the median preferable over the mean?
A. When the data is normally distributed
B. When all scores are equal
C. When the data is skewed
D. When standard deviation is low
Answer: C - Which of the following is a graphical representation that shows cumulative frequency?
A. Histogram
B. Ogive
C. Frequency polygon
D. Pie chart
Answer: B - If a distribution has high kurtosis, it is said to be:
A. Flat
B. Positively skewed
C. Peaked
D. Normal
Answer: C - Which of the following is used to compare the scores of different tests having different units?
A. Percentile
B. Raw score
C. Derived score
D. Mode
Answer: C - The coefficient of determination (r²) represents:
A. Total variability
B. Unexplained variation
C. Explained variance
D. Mean deviation
Answer: C - Which of the following measures is most affected by extreme values?
A. Median
B. Mode
C. Mean
D. Interquartile Range
Answer: C - Which of the following is true about Spearman’s rank correlation coefficient?
A. It assumes normal distribution
B. It is sensitive to outliers
C. It uses ordinal data
D. It is used for interval data only
Answer: C - The midpoint of a class interval in a frequency table is called:
A. Class width
B. Frequency
C. Midpoint
D. Class mark
Answer: D - Which of the following shows the relationship between two variables and is used in correlation studies?
A. Ogive
B. Scatter plot
C. Histogram
D. Line graph
Answer: B - Which term refers to the difference between the highest and lowest scores?
A. Variance
B. Range
C. Standard deviation
D. Mode
Answer: B - If the mean is greater than the median, the distribution is likely to be:
A. Normal
B. Negatively skewed
C. Positively skewed
D. Symmetrical
Answer: C - A test score that is one SD above the mean in a normal distribution corresponds to which percentile (approx)?
A. 50th
B. 68th
C. 84th
D. 95th
Answer: C - A T-score is calculated from a Z-score using the formula:
A. T = 10Z + 50
B. T = 5Z + 100
C. T = Z × 50
D. T = Z + 100
Answer: A - Which score is the least stable as a measure of central tendency?
A. Mode
B. Median
C. Mean
D. Midrange
Answer: A - Which concept allows meaningful comparisons of scores across different tests?
A. Raw scores
B. Cumulative frequencies
C. Standard scores
D. Frequency tables
Answer: C