1. Which formula is used to calculate the coefficient of skewness based on mean, median, and standard deviation?

A. \(\text{Skewness} = \frac{3(\text{Mean} - \text{Median})}{S}\) B. \(\text{Skewness} = \frac{\text{Mean} - \text{Median}}{S}\) C. \(\text{Skewness} = \frac{\text{Median} - \text{Mean}}{S}\) D. \(\text{Skewness} = \frac{\text{Mode} - \text{Mean}}{S}\)

2. The coefficient of variation (C.V) is given by:

A. \(\frac{\bar{X}}{S} \times 100\%\) B. \(\frac{S}{\bar{X}} \times 100\%\) C. \(S \times \bar{X} \times 100\%\) D. \(\frac{S^2}{\bar{X}} \times 100\%\)

3. Which type of mean is the Nth root of the product of N positive numbers?

A. Harmonic Mean B. Arithmetic Mean C. Geometric Mean D. Mode

4. The deciles divide data into how many equal parts?

A. 4 B. 5 C. 10 D. 100

5. Data with low kurtosis (platykurtic) tend to have:

A. Sharp peak near the mean B. Flat top near the mean C. No tails D. No deviation

6. Which of the following statements about the geometric mean is correct?

A. It is always greater than or equal to the arithmetic mean B. It is always less than or equal to the harmonic mean C. It is always less than or equal to the arithmetic mean but greater than or equal to the harmonic mean D. It is the simple average of a data set

7. Which measure of dispersion has the same units as the data?

A. Variance B. Mean Deviation C. Skewness D. Kurtosis

8. Which of the following is NOT a measure of location?

A. Median B. Mode C. Variance D. Mean

9. What does the skewness measure in a data distribution?

A. The average value of the data B. The degree of spread in the data C. The asymmetry or departure from symmetry of the distribution D. The peak height of the distribution

10. Which measure of dispersion is calculated as the square root of the variance?

A. Mean Deviation B. Standard Deviation C. Coefficient of Variation D. Range

11. How is standard deviation related to variance?

A. Standard deviation is the square of variance B. Standard deviation is the square root of variance C. Standard deviation is double the variance D. Standard deviation is half the variance

12. In the empirical relationship for moderately skewed unimodal distributions, which formula represents Mean – Mode?

A. 3(Mean – Median) B. Mean + Median + Mode C. Mean – Median = Mode D. Mode – Mean = 3(Median – Mean)

13. If data is positively skewed, which is the correct order of mean, median, and mode?

A. Mode > Median > Mean B. Mode < Median < Mean C. Mean = Median = Mode D. Median < Mean < Mode

14. Which of the following inequalities indicates positive skewness?

A. Mean < Median < Mode B. Mode < Median < Mean C. Mean = Median = Mode D. Mode > Median > Mean

15. The empirical relationship between mean, median and mode is expressed as:

A. \(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\) B. \(\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})\) C. \(\text{Mean} = \frac{\text{Median} + \text{Mode}}{2}\) D. \(\text{Median} = \text{Mean} - \text{Mode}\)

16. What is the formula for the arithmetic mean of grouped data using class midpoints?

A. \(\bar{X} = \frac{\sum fX}{N}\) B. \(\bar{X} = \frac{\sum X}{N}\) C. \(\bar{X} = \sqrt[N]{\prod X_i}\) D. \(\bar{X} = \frac{\sum f}{N}\)

17. What is indicated by a coefficient of variation (C.V) of 100%?

A. No variability in the data B. The standard deviation is equal to the mean C. Data is negatively skewed D. Mean is zero

18. Which method simplifies mean calculation by using an assumed mean \(A\)?

A. Harmonic mean method B. Geometric mean method C. Assumed mean method D. Mode estimation

19. What kurtosis value corresponds to a normal distribution?

A. 0 B. 1 C. 3 D. 5

20. What defines a bimodal distribution?

A. A distribution with no modes B. A distribution with two modes C. A distribution where mean = median = mode D. A distribution with one mode

21. Mean Deviation is defined as:

A. The average of squared deviations from the mean B. The average absolute deviations from the mean C. The maximum minus minimum value D. The square root of variance

22. The kurtosis of a data distribution measures:

A. The asymmetry of the data B. The peakness or flatness relative to a normal distribution C. The central tendency of the data D. The relative spread of the data

23. The mode of grouped data is estimated using which formula?

A. \( \text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times w \) B. \( \text{Mode} = \bar{X} + 3(\bar{X} - \text{Median})\) C. \( \text{Mode} = \text{Median} + \frac{f_1}{f_0 + f_2} \) D. \( \text{Mode} = L + \frac{f_1}{f_0 + f_2} \times w \)

24. Which measure of location is defined as the sum of all observations divided by the number of observations?

A. Median B. Mode C. Arithmetic Mean D. Geometric Mean

25. What divides data into hundred equal parts?

A. Deciles B. Quartiles C. Percentiles D. Modes

26. Using the assumed mean method, the mean is given by:

A. \(\bar{X} = A + \frac{\sum fd}{\sum f}\) where \(d = X - A\) B. \(\bar{X} = A - \frac{\sum fd}{\sum f}\) C. \(\bar{X} = \frac{\sum fX}{N}\) D. \(\bar{X} = \sqrt[N]{\prod X_i}\)

27. Which measure of dispersion is defined as the difference between the largest and smallest values in a dataset?

A. Range B. Mean Deviation C. Variance D. Standard Deviation

28. How do you calculate the first quartile \(Q_1\) in grouped data?

A. \(Q_1 = L + \frac{\frac{N}{4} - F}{f} \times w\) B. \(Q_1 = L + \frac{\frac{N}{2} - F}{f} \times w\) C. \(Q_1 = L + \frac{\frac{3N}{4} - F}{f} \times w\) D. \(Q_1 = L + \frac{N - F}{f} \times w\)

29. A negative skewness value indicates that the data distribution is:

A. Symmetric B. Skewed to the right C. Skewed to the left D. Uniformly distributed

30. Which formula represents the coefficient of skewness based on mean, median, and standard deviation?

A. (Mean – Mode) / Standard Deviation B. 3(Mean – Median) / Standard Deviation C. Mode / Mean D. Standard Deviation / Mean

31. Kurtosis measures:

A. Central tendency of data B. The symmetry of the distribution C. The peakedness or flatness of the distribution relative to normal distribution D. Variability in the data

32. The semi-interquartile range (quartile deviation) is:

A. \( \frac{Q_3 + Q_1}{2} \) B. \( \frac{Q_3 - Q_1}{2} \) C. \(Q_3 - Q_1\) D. \(Q_1 - Q_3\)

33. The semi-interquartile range measures:

A. Total spread of the data B. Average deviation of the data points from the mean C. Half the distance between the third and first quartiles D. The difference between the maximum and minimum values

34. The harmonic mean is defined as:

A. The average of the values themselves B. The reciprocal of the arithmetic mean of the reciprocals of the values C. The geometric average of the values D. The difference between the maximum and minimum values

35. What characterizes a unimodal frequency curve?

A. It has exactly one mode B. It has two or more modes C. The mode is always equal to the median D. The data is always normally distributed

36. The Interquartile Range (IQR) is:

A. \(Q_3 + Q_1\) B. \(Q_3 - Q_1\) C. \(Q_1 - Q_3\) D. \(\frac{Q_3 - Q_1}{2}\)

37. Excess kurtosis is defined as:

A. \(K - 1\) B. \(K - 2\) C. \(K - 3\) D. \(3 - K\)

38. How are percentiles used in describing data?

A. They divide the data into ten equal parts B. They divide the data into four equal parts C. They divide the data into hundred equal parts D. They divide the data into halves

39. What is true about data sets with high kurtosis?

A. They have a flat peak and thin tails B. They tend to be uniformly distributed C. They have a distinct peak near the mean and heavy tails D. They always have zero skewness

40. The \(P_k\)th percentile in grouped data is found using the formula:

A. \(L + \frac{\frac{k}{100}N - F}{f} \times w\) B. \(L + \frac{F - \frac{k}{100}N}{f} \times w\) C. \(L + \frac{f - \frac{k}{100}N}{F} \times w\) D. \(L + \frac{N - F}{f} \times w\)

41. Negative skewness indicates:

A. Data skewed to the right (positive skew) B. Data skewed to the left (negative skew) C. Symmetric data D. Data with heavy tails

42. The variance of a dataset is:

A. The mean of the data B. The average squared deviation from the mean C. The square root of standard deviation D. The difference between maximum and minimum values

43. Which percentile represents the middle value of data?

A. 25th percentile B. 50th percentile C. 75th percentile D. 90th percentile

44. For a perfectly symmetric distribution, the relationship between mean, median, and mode is:

A. Mean < Median < Mode B. Mode < Median < Mean C. Mean = Median = Mode D. Mean > Median > Mode

45. How is the variance of a grouped data set calculated?

A. Average of the numbers B. Sum of squared deviations from the mean divided by the total frequency C. Difference between highest and lowest value D. Difference between mean and mode

46. What does a skewness value of zero indicate about a distribution?

A. Left skewed B. Right skewed C. Symmetric distribution D. Flat distribution

47. What does the coefficient of variation (C.V) express?

A. The absolute variation in the data B. The ratio of variance to mean C. The relative variation expressed as a percentage of the mean D. The sum of all deviations from the mean

48. In frequency distributions, the median class is the class interval:

A. With the highest frequency B. Containing the middle observation when data is arranged C. With the smallest width D. With zero frequency

49. In grouped data, what is the 'class mark'?

A. The boundary between two classes B. The frequency of the class interval C. The midpoint of the class interval D. The cumulative frequency up to the class

50. The mean absolute deviation from the center is known as:

A. Range B. Mean Deviation C. Variance D. Skewness