1. Which of the following is NOT a measure of dispersion?

A. Range B. Mean deviation C. Mode D. Standard deviation

2. The median of grouped data can be obtained using:

A. The average of highest and lowest values B. Simple counting of frequency C. \( \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times w \) D. \( \text{Median} = \frac{\sum x}{N} \)

3. The arithmetic mean is best described as:

A. The Nth root of the product of values B. The sum of values divided by the number of values C. The middle value when data is arranged D. The value that appears most frequently

4. Which measure of central tendency is most affected by extreme values in a skewed distribution?

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

5. How is the median class identified in a grouped frequency distribution?

A. The class with the highest frequency B. The class where cumulative frequency first exceeds half the total frequency C. The middle class interval by range D. The class with the lowest frequency

6. The range is defined as:

A. The difference between the largest and smallest values in the dataset B. The average value of a dataset C. The product of the largest and smallest values D. The sum of the variances

7. Which of the following measures how flat or peaked a distribution is?

A. Skewness B. Kurtosis C. Range D. Mean deviation

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

A. Variance B. Standard deviation C. Skewness D. Kurtosis

9. If a data distribution is positively skewed, which of the following is true?

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

10. What does the coefficient of variation (C.V) measure in a data set?

A. The absolute difference between the mean and median B. The ratio of the standard deviation to the mean expressed as a percentage C. The skewness of the distribution D. The range between the maximum and minimum values

11. Which measure of location is defined as the value that occurs most frequently in a dataset?

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

12. What does mesokurtic distribution indicate?

A. A distribution more peaked than normal B. A normal distribution shape C. A distribution flatter than normal D. A skewed distribution

13. The standard deviation is defined as:

A. The average deviation from the median B. The square root of the variance C. The square of the variance D. The difference between max and min values

14. What is the purpose of using an assumed mean in mean calculation?

A. To simplify computation when values are large B. To find the median easily C. To calculate variance directly D. To find mode faster

15. What is the kurtosis value for a normal distribution?

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

16. The geometric mean is:

A. The arithmetic mean of the logs of data B. The Nth root of the product of N values C. The sum of scores divided by frequency D. The average absolute deviation from mean

17. Which percentile divides data into 100 equal parts?

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

18. What is the value of skewness for a perfectly symmetric distribution?

A. 1 B. 0 C. -1 D. Infinity

19. Leptokurtic distributions have:

A. A flat top compared to normal B. A distinct sharp peak relative to normal C. Same kurtosis as normal D. No variation

20. The 90th percentile minus the 10th percentile gives:

A. Range B. Semi-interquartile range C. 10-90 percentile range D. Variance

21. What is the meaning of a semi-interquartile range in a data set?

A. The range between minimum and maximum values B. Half the difference between the third quartile (Q3) and first quartile (Q1) C. The sum of first and third quartiles D. The difference between median and mode

22. What does the variance of a dataset represent?

A. The average of absolute deviations from the median B. The average squared deviation from the mean C. The difference between max and min values D. The square root of the standard deviation

23. The interquartile range (IQR) is the difference between:

A. 10th and 90th percentile B. Quartile 1 and Quartile 3 C. Median and Mode D. Maximum and Minimum

24. When the data distribution is platykurtic, what does it look like compared to a normal distribution?

A. It has a sharper and taller peak B. It has heavier tails C. It has a flatter and broader peak D. It is perfectly symmetrical

25. The coefficient of variation (C.V) is defined as?

A. Ratio of mean to standard deviation × 100% B. Ratio of standard deviation to mean × 100% C. Standard deviation minus mean D. Mean minus standard deviation

26. Platykurtic distributions are:

A. More peaked than normal B. Less peaked or flat-topped relative to normal C. Equivalent to normal D. Skewed distributions

27. The formula Mean - Mode = 3(Mean - Median) is used to describe what?

A. The relationship in a perfectly symmetric distribution B. The empirical relationship between mean, median, and mode in a moderately skewed unimodal distribution C. The formula for kurtosis D. The calculation of harmonic mean

28. If a data set has mean = median = mode, what can be inferred about its skewness?

A. It is positively skewed B. It is negatively skewed C. It is symmetric with zero skewness D. It has high kurtosis

29. What does a positive skewness value indicate about the relative positions of mean, median, and mode?

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

30. Which of the following formulas is used for the mode in grouped data?

A. \( \text{Mode} = L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times w \) B. \( \text{Mode} = \frac{L + w}{f} \) C. \( \text{Mode} = \text{Median} \times 2 - \text{Mean} \) D. \( \text{Mode} = \frac{\sum f x}{\sum f} \)

31. What does a negative skewness indicate about the distribution of data?

A. The data are skewed to the right B. Mean < Median < Mode (skewed left) C. Mode < Median < Mean D. The data have no skewness

32. How is excess kurtosis defined?

A. Kurtosis minus 3 B. Kurtosis plus 3 C. Variance minus 3 D. Skewness squared

33. Which of the following is a property of a symmetric distribution?

A. Skewness is positive B. Skewness is zero C. Kurtosis is negative D. Mode > mean

34. What is the formula for coefficient of skewness given mean, median, and standard deviation?

A. \( \frac{\text{mean} - \text{median}}{\sigma} \) B. \( \frac{3(\text{mean} - \text{median})}{\sigma} \) C. \( \frac{\text{mode} - \text{mean}}{\sigma} \) D. \( \frac{\text{variance}}{\text{mean}} \)

35. Which of the following best describes the relationship between the geometric mean and the arithmetic mean for a set of positive numbers?

A. Geometric mean is always greater than the arithmetic mean B. Geometric mean is always less than or equal to the arithmetic mean C. Geometric mean equals the arithmetic mean squared D. Geometric mean and arithmetic mean are unrelated

36. What does a negative skewness value indicate?

A. Data skewed to the right B. Data is symmetric C. Data skewed to the left D. Data with no mode

37. What happens to variance when the data points are all the same?

A. Variance is high B. Variance is zero C. Variance is negative D. Variance is equal to mean

38. What characteristic of a distribution is described by kurtosis?

A. The central tendency or average B. The symmetry of the distribution C. The peakedness or flatness relative to a normal distribution D. The spread between the minimum and maximum values

39. Which measure divides a dataset into four equal parts?

A. Deciles B. Percentiles C. Quartiles D. Mean deviation

40. Deciles divide data into how many equal parts?

A. 4 B. 10 C. 100 D. 2

41. What is the relationship between standard deviation and variance?

A. Variance is the square root of standard deviation B. Variance is the mean of standard deviation C. Standard deviation is the square root of variance D. No relationship

42. To calculate variance for grouped data, which quantities do you need?

A. Class boundaries and mode B. Frequencies, midpoints, and mean C. Only the frequencies D. Only the midpoints

43. What is the definition of statistics in terms of data?

A. A branch of mathematics dealing purely with theoretical numbers B. A discipline for collection, organization, summarization, and interpretation of data C. The study of probabilities only D. A method of writing scientific papers

44. Excess kurtosis is calculated by subtracting 3 from the kurtosis value. What does an excess kurtosis of zero imply?

A. The distribution is platykurtic (flat-topped) B. The distribution is mesokurtic (normal) C. The distribution is leptokurtic (peaked) D. The distribution is bimodal

45. What is the empirical relationship between mean, median, and mode in a moderately skewed distribution?

A. Mean - Mode = 3(Mean - Median) B. Mode = Median + Mean C. Median = (Mean + Mode)/2 D. Mode = Mean - Median

46. In a frequency distribution, which of the following formulas is used to estimate the mode from grouped data?

A. Mode = Lower class boundary + (difference between modal class frequency and previous class frequency)/sum of differences × class width B. Mode = Median + 3(Mean - Median) C. Mode = Arithmetic mean of mid-points D. Mode = Mid-point of the largest class interval

47. Mean deviation is:

A. The mean of absolute deviations from the mean B. The average of squared deviations from the mean C. Median minus mode D. Range divided by 2

48. The semi-interquartile range is:

A. The average of Q1 and Q3 B. Half the interquartile range C. Difference between the median and mode D. Twice the variance

49. Which measure of dispersion is defined as the average of the squared deviations from the mean?

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

50. For grouped data, the mean can be calculated as:

A. \( \bar{X} = \frac{\sum f x}{\sum f} \) B. \( \bar{X} = \frac{L + w}{f} \) C. \( \bar{X} = \text{Median} \times 2 - \text{Mode} \) D. \( \bar{X} = \sqrt{\sum f x^2} \)