1. What is the formula for the mean of grouped data using the direct method?
   a)

   $x = \frac{\sum f}{\sum x}$

   
   b)

   $x = \frac{\sum fx}{\sum f}$

   
   c)

   $x = \frac{\sum f^2}{\sum fx}$

   
   d)

   $x = \frac{\sum x}{\sum f}$

   x=∑f∑x
   Answer: b

2. The sum of the frequencies in a frequency distribution is called:
   a) Mode
   b) Median
   c) Cumulative frequency
   d) Total frequency
   Answer: d

3. In statistics, the most frequently occurring value in a dataset is called:
   a) Mean
   b) Median
   c) Mode
   d) Variance
   Answer: c

4. What is the midpoint of the class interval 40-50?
   a) 40
   b) 45
   c) 50
   d) 90
   Answer: b

5. The median is:
   a) The sum of all values divided by the number of values
   b) The middle value when data is arranged in order
   c) The most frequently occurring value
   d) The highest value minus the lowest value
   Answer: b

6. What is the full form of the symbol Σ in statistics?

   a) Difference
   b) Summation
   c) Product
   d) Division
   Answer: b

7. The mode of a dataset is useful when we need to find:
   a) The average value
   b) The most common value
   c) The range
   d) The standard deviation
   Answer: b

8. The formula to calculate the mode in grouped data is:
   a)

   $\text{Mode} = l + \frac{(f_1 – f_0)}{(2f_1 – f_0 – f_2)} \times h$

   
   b)

   $\text{Mode} = \frac{\sum fx}{\sum f}$

   
   c)

   $\text{Mode} = \frac{f_1 + f_2}{f_0}$

   
   d)

   $\text{Mode} = \frac{\sum f}{N}$

   
   Answer: a

9. The cumulative frequency of a class is:
   a) The sum of all previous class frequencies including the given class
   b) The difference of class frequencies
   c) The product of class limits
   d) The highest frequency in the dataset
   Answer: a

10. If the class interval is 10-20, then the lower boundary is:
    a) 10
    b) 15
    c) 20
    d) 25
    Answer: a

Moderate Level (16-35):
11. If the mode of a distribution is 45 and the mean is 50, then the median using the empirical relation is:
a) 55
b) 48.33
c) 47.5
d) 50.5
Answer: c

12. What is the assumed mean method used for?
    a) Simplifying mean calculations
    b) Calculating mode
    c) Finding standard deviation
    d) Finding class intervals
    Answer: a

13. If a dataset contains outliers, which measure of central tendency is least affected?
    a) Mean
    b) Median
    c) Mode
    d) Range
    Answer: b

14. What does “ogive” represent in statistics?
    a) Cumulative frequency curve
    b) Mean deviation
    c) Frequency polygon
    d) Bar graph
    Answer: a

15. The step-deviation method is useful when:
    a) Data values are small
    b) Data values are large
    c) Data is ungrouped
    d) Data has a low frequency
    Answer: b

16. If the class size is 10, and the assumed mean is 50, what is the deviation of 70?
    a) 2
    b) -2
    c) 20
    d) -20
    Answer: a

17. The median divides the dataset into:
    a) Two equal halves
    b) Three equal parts
    c) Four equal parts
    d) Five equal parts
    Answer: a

18. In an ogive, the x-axis represents:
    a) Frequency
    b) Cumulative frequency
    c) Class intervals
    d) Data points
    Answer: c

19. The sum of all frequencies in a grouped data table is known as:
    a) Frequency polygon
    b) Median class
    c) Total frequency
    d) Class boundary
    Answer: c

20. If the mean of a dataset is 60, and the sum of all values is 600, what is the number of observations?
    a) 10
    b) 20
    c) 30
    d) 40
    Answer: b

21. What is the formula for mean in the step-deviation method?

    a)

    $x = a + \frac{\sum f u}{\sum f} \times h$

    
    b)

    $x = a – \frac{\sum f d}{\sum f}$

    
    c)

    $x = a + \frac{\sum f x}{\sum f}$

    
    d)

    $x = \frac{\sum f d}{\sum f} + a$

    
    Answer: a

    22. If a dataset has two modes, it is called:
        a) Unimodal
        b) Bimodal
        c) Trimodal
        d) Multimodal
        Answer: b

    23. The median class is determined by:
        a) The highest frequency
        b) Cumulative frequency closest to n/2
        c) The lowest frequency
        d) The mean value
        Answer: b

    24. A positively skewed distribution has:
        a) Mean < Median < Mode
        b) Mean > Median > Mode
        c) Mean = Mode = Median
        d) None of the above
        Answer: b

    25. In a normal distribution, which measure of central tendency is highest?
        a) Mean
        b) Median
        c) Mode
        d) All are equal
        Answer: d

    26. What does the sum of all class frequencies represent?

        a) Mode
        b) Mean
        c) Total number of observations
        d) Median
        Answer: c

        27. In a histogram, the area of each rectangle is proportional to:
            a) Class frequency
            b) Class interval
            c) Cumulative frequency
            d) Mean
            Answer: a

        28. The median of a dataset is found by:
            a) Arranging data and finding the middle value
            b) Adding all values and dividing by their count
            c) Finding the most frequently occurring value
            d) Using the formula

            $x = \frac{\sum fx}{\sum f}$

            
            Answer: a

        29. The empirical relation between mean, median, and mode is:
            a)

            $\text{Mode} = 3 \times \text{Median} – 2 \times \text{Mean}$

            
            b)

            $\text{Mean} = 3 \times \text{Mode} – 2 \times \text{Median}$

            
            c)

            $\text{Median} = 3 \times \text{Mean} – 2 \times \text{Mode}$

            
            d) None of these
            Answer: a

        30. If the mean of a dataset is 40 and the number of observations is 10, what is the sum of the data values?
            a) 40
            b) 400
            c) 4
            d) 100
            Answer: b

        31. In a continuous frequency distribution, the median class is the one where:

            a) Cumulative frequency is exactly n/2
            b) Cumulative frequency is closest but greater than n/2
            c) The class has the highest frequency
            d) The difference between class limits is minimum
            Answer: b

            32. The mean of five numbers is 20. If one number is removed, the new mean is 18. What is the removed number?
                a) 20
                b) 25
                c) 30
                d) 35
                Answer: c

            33. What does the term “cumulative frequency” mean?
                a) Sum of all previous frequencies
                b) Highest class frequency
                c) Mode of the dataset
                d) Difference between class frequencies
                Answer: a

            34. The mode of a grouped frequency distribution is found in which class?
                a) Median class
                b) Class with the highest frequency
                c) Class with the lowest frequency
                d) None of the above
                Answer: b

            35. What is the mean of the first 10 natural numbers?
                a) 5
                b) 5.5
                c) 6
                d) 7
                Answer: b

            36. The step deviation method is most useful when:
                a) The class size is unequal
                b) The class size is large and equal
                c) The data is ungrouped
                d) The mean is already known
                Answer: b

            37. If the median of a dataset is 50, what percentage of the data lies below this value?
                a) 25%
                b) 50%
                c) 75%
                d) 100%
                Answer: b

            38. In a positively skewed distribution:
                a) Mean > Median > Mode
                b) Mode > Median > Mean
                c) Mean = Mode = Median
                d) None of these
                Answer: a

            39. If the mode is 36 and the mean is 42, what is the approximate median?
                a) 39
                b) 40
                c) 41
                d) 42
                Answer: b

            40. Which measure of central tendency is best for highly skewed data?
                a) Mean
                b) Median
                c) Mode
                d) Range
                Answer: b

            41. The mean of a frequency distribution is 50, and the assumed mean is 48 with a class width of 5. The sum of deviations is 20, and the total frequency is 10. Find the actual mean.

                a) 50
                b) 49
                c) 51
                d) 52
                Answer: b

                42. The median is 60, the mode is 54, and the mean is unknown. What is the mean using the empirical formula?
                    a) 58
                    b) 60
                    c) 62
                    d) 64
                    Answer: a

                43. If all data values in a dataset are increased by 5, how is the mean affected?
                    a) Increases by 5
                    b) Decreases by 5
                    c) Remains unchanged
                    d) Doubles
                    Answer: a

                44. If the mean is 30 and all values are doubled, the new mean will be:
                    a) 30
                    b) 60
                    c) 90
                    d) 120
                    Answer: b

                45. A frequency distribution has a mode of 55 and a median of 58. What is the mean?
                    a) 60
                    b) 59
                    c) 61
                    d) 62
                    Answer: c

                46. If the median of a dataset is 35, then approximately what fraction of the data lies above this value?
                    a) 1/4
                    b) 1/3
                    c) 1/2
                    d) 3/4
                    Answer: c

                47. If the median class is 40-50 and the cumulative frequency before this class is 30, while its frequency is 20, what is the median position?
                    a) 30
                    b) 35
                    c) 40
                    d) 45
                    Answer: d

                48. In the step deviation method, if the class size is 10 and the deviations are -3, -2, 0, 2, 3, what is the sum of deviations?
                    a) 0
                    b) 5
                    c) -5
                    d) 10
                    Answer: a

                49. If a dataset is negatively skewed, which of the following is true?
                    a) Mean < Median < Mode
                    b) Mean > Median > Mode
                    c) Mean = Median = Mode
                    d) None of the above
                    Answer: a

                50. If the mean of a dataset is 75 and the standard deviation is 5, what is the coefficient of variation?
                    a) 6.67%
                    b) 5%
                    c) 10%
                    d) 15%
                    Answer: a