Q.1 What does skewness measure in a distribution?
Central tendency
Asymmetry
Peakedness
Dispersion
Explanation - Skewness measures the degree of asymmetry in the frequency distribution of data.
Correct answer is: Asymmetry
Q.2 If a distribution has a long right tail, it is said to be:
Negatively skewed
Positively skewed
Symmetrical
Mesokurtic
Explanation - A right tail indicates positive skewness, meaning most data is concentrated on the left.
Correct answer is: Positively skewed
Q.3 What is the skewness of a perfectly symmetrical distribution?
0
1
-1
Undefined
Explanation - In a perfectly symmetrical distribution, skewness is zero.
Correct answer is: 0
Q.4 If mean > median > mode, the distribution is:
Symmetrical
Positively skewed
Negatively skewed
Platykurtic
Explanation - When mean is greater than median and mode, the tail is longer on the right, indicating positive skewness.
Correct answer is: Positively skewed
Q.5 Which measure indicates the flatness or peakedness of a distribution?
Skewness
Variance
Kurtosis
Standard deviation
Explanation - Kurtosis measures the shape of a distribution, specifically whether it is peaked or flat relative to a normal distribution.
Correct answer is: Kurtosis
Q.6 A normal distribution has kurtosis equal to:
0
1
3
-3
Explanation - For normal distribution, the kurtosis is 3 (mesokurtic).
Correct answer is: 3
Q.7 What type of kurtosis does a distribution with heavy tails have?
Leptokurtic
Platykurtic
Mesokurtic
Skewed
Explanation - Leptokurtic distributions have sharper peaks and heavier tails than normal distributions.
Correct answer is: Leptokurtic
Q.8 In a negatively skewed distribution, which is true?
Mean < Median < Mode
Mean > Median > Mode
Mean = Median = Mode
Median > Mode > Mean
Explanation - In negatively skewed data, the mean is less than the median, which is less than the mode.
Correct answer is: Mean < Median < Mode
Q.9 Which formula is used to calculate Karl Pearson’s coefficient of skewness?
(Mean - Mode)/SD
(Mean - Median)/Range
Mode - Median
(Q3 - Q1)/2
Explanation - Karl Pearson’s coefficient of skewness is (Mean - Mode)/Standard Deviation.
Correct answer is: (Mean - Mode)/SD
Q.10 What does a skewness value of -0.8 indicate?
Symmetrical distribution
Mild positive skew
Moderate negative skew
High peakedness
Explanation - A negative skewness value indicates left skewness. -0.8 indicates moderate asymmetry.
Correct answer is: Moderate negative skew
Q.11 If skewness is exactly 0, kurtosis is 3, then the distribution is:
Leptokurtic
Platykurtic
Normal
Asymmetrical
Explanation - A normal distribution has skewness 0 and kurtosis 3.
Correct answer is: Normal
Q.12 Which of the following is NOT a measure of skewness?
Karl Pearson’s method
Bowley’s method
Kelly’s method
Fisher’s kurtosis method
Explanation - Kurtosis measures peakedness, not skewness. Pearson, Bowley, and Kelly are skewness methods.
Correct answer is: Fisher’s kurtosis method
Q.13 What does a positive kurtosis value indicate compared to normal distribution?
Flatter
More peaked
Perfectly symmetrical
Left skewed
Explanation - Positive kurtosis indicates a distribution with heavier tails and sharper peak (leptokurtic).
Correct answer is: More peaked
Q.14 Bowley’s coefficient of skewness uses:
Mean and Median
Quartiles and Median
Variance and Mode
Standard Deviation
Explanation - Bowley’s measure uses Q1, Q3, and median to calculate skewness.
Correct answer is: Quartiles and Median
Q.15 A platykurtic distribution is:
More flat than normal
More peaked than normal
Equal to normal
Always positively skewed
Explanation - Platykurtic distributions are flatter and have lighter tails than the normal distribution.
Correct answer is: More flat than normal
Q.16 In Karl Pearson’s method, if mode is ill-defined, which relation is used?
Mode = 3Median - 2Mean
Mean = Median + Mode
Median = (Mean+Mode)/2
Mode = Mean
Explanation - When mode is not defined, Pearson’s empirical relation Mode = 3Median - 2Mean is applied.
Correct answer is: Mode = 3Median - 2Mean
Q.17 Which type of distribution has kurtosis less than 3?
Leptokurtic
Platykurtic
Mesokurtic
Normal
Explanation - Platykurtic distributions have kurtosis < 3 and are flatter than normal.
Correct answer is: Platykurtic
Q.18 If a dataset is symmetrical, which of the following is true?
Mean = Median = Mode
Mean > Median > Mode
Median < Mode < Mean
Skewness > 0
Explanation - In a symmetrical distribution, mean, median, and mode coincide.
Correct answer is: Mean = Median = Mode
Q.19 Kelly’s coefficient of skewness is based on:
Deciles and percentiles
Mean and mode
Quartiles and median
Variance
Explanation - Kelly’s method uses deciles and percentiles for skewness.
Correct answer is: Deciles and percentiles
Q.20 Which of the following is a limitation of kurtosis?
Difficult to compute
Does not indicate skewness
Depends only on mean
Not used in finance
Explanation - Kurtosis measures peakedness, not asymmetry; hence it does not indicate skewness.
Correct answer is: Does not indicate skewness
Q.21 The skewness of a normal distribution is:
0
1
3
Depends on variance
Explanation - Normal distribution is symmetric, so its skewness is 0.
Correct answer is: 0
Q.22 What does a skewness value close to 0 indicate?
Distribution is symmetric
Distribution is highly skewed
Distribution is leptokurtic
Distribution is flat
Explanation - A skewness close to 0 suggests that the distribution is approximately symmetric.
Correct answer is: Distribution is symmetric
Q.23 Which measure is more influenced by extreme values when measuring skewness?
Median
Mode
Mean
Quartiles
Explanation - The mean is sensitive to extreme values, making it highly influential in skewness measurement.
Correct answer is: Mean
Q.24 What is excess kurtosis of a normal distribution?
0
3
-3
1
Explanation - Excess kurtosis = Kurtosis - 3. For normal distribution, it is 0.
Correct answer is: 0
Q.25 Which distribution has more outliers: leptokurtic or platykurtic?
Leptokurtic
Platykurtic
Both equal
Cannot be determined
Explanation - Leptokurtic distributions have heavier tails and therefore more extreme outliers.
Correct answer is: Leptokurtic