Knowledge Check : Statistics
Knowledge Check – Statistics
1. Collection and Organisation of Data (Q1–Q20)
Q1: In a survey of favourite fruits among 40 students, mango is liked by 12 students. The frequency of mango is
A) 12
B) 28
C) 40
D) 52
Q2: Tally marks for the number 23 are correctly represented as
A) |||| |||| |||| |||| ||
B) |||| |||| |||| |||| |||
C) |||| |||| |||| |||| |||| |||
D) |||| |||| |||| |||| |||| ||
Q3: For the class interval 30–40, the class mark is
A) 30
B) 35
C) 40
D) 70
Q4: The lower limit of the class 50–60 is
A) 49.5
B) 50
C) 50.5
D) 60
Q5: In exclusive class intervals 10–20, 20–30, the observation 20 belongs to the class
A) 10–20
B) 20–30
C) Both
D) None
Q6: The class width (size) of the interval 25–35 is
A) 9
B) 10
C) 11
D) 35
Q7: Unprocessed marks of students directly recorded from answer sheets are called
A) Grouped data
B) Raw data
C) Frequency table
D) Cumulative frequency
Q8: In a frequency distribution table, Σf represents
A) Total frequency
B) Average
C) Class width
D) Number of classes
Q9: For drawing a histogram, class intervals must be
A) Inclusive
B) Exclusive or continuous
C) Open-ended
D) Unequal
Q10: The ideal number of classes for 120 students’ marks is approximately
A) 5–7
B) 8–12
C) 15–20
D) 20–25
Q11: Class intervals 0–10, 10–20, 20–30 are of the type
A) Inclusive
B) Exclusive
C) Irregular
D) Open
Q12: The upper limit of the class 70–80 is
A) 70
B) 75
C) 80
D) 79.5
Q13: In a grouped frequency distribution, the class having maximum frequency is called
A) Median class
B) Modal class
C) Mean class
D) First class
Q14: Raw data of heights (in cm): 152, 155, 152, 158, 160, 155, 152. Frequency of 152 cm is
A) 2
B) 3
C) 4
D) 5
Q15: Class boundaries for inclusive class 20–29 are
A) 20–29
B) 19.5–29.5
C) 20.5–28.5
D) 20–30
Q16: The class interval with highest frequency in marks distribution of a school is 60–70. This class is
A) Median class
B) Modal class
C) First class
D) Last class
Q17: In a frequency table, if Σfᵢxᵢ is needed, xᵢ represents
A) Frequency
B) Class mark
C) Lower limit
D) Cumulative frequency
Q18: For 200 families surveyed, the most suitable number of classes is
A) 6–8
B) 10–14
C) 15–20
D) 25–30
Q19: Data arranged in classes is called
A) Raw data
B) Grouped data
C) Discrete data
D) Continuous series
Q20: The correct tally representation for frequency 31 is
A) |||| |||| |||| |||| |||| |||| |
B) |||| |||| |||| |||| |||| |||| ||
C) |||| |||| |||| |||| |||| |||| |||
D) |||| |||| |||| |||| |||| |||| ||||
2. Graphical Representation of Data (Q21–Q40)
Q21: In a pictograph, one bicycle symbol represents 20 bicycles sold. To show 120 bicycles, the number of complete symbols needed is
A) 4
B) 5
C) 6
D) 8
Q22: Which of the following graphs must have no gaps between the bars?
A) Bar graph
B) Double bar graph
C) Histogram
D) Frequency polygon
Q23: To compare the marks of boys and girls in a class over 5 months, the most suitable graph is
A) Simple bar graph
B) Double bar graph
C) Pie chart
D) Pictograph
Q24: Frequency polygon is constructed by joining the
A) Lower corners of histogram bars
B) Mid-points of the tops of histogram bars
C) Upper corners of histogram bars
D) Centres of the bases
Q25: In a pie chart, a central angle of 90° represents what percentage of the total?
A) 20%
B) 25%
C) 30%
D) 36%
Q26: If one star in a pictograph represents 500 kg of rice, then half star represents
A) 100 kg
B) 250 kg
C) 500 kg
D) 1000 kg
Q27: Histogram is not suitable for
A) Continuous data
B) Discrete data with large gaps
C) Grouped frequency distribution
D) Height of students
Q28: The width of each bar in a bar graph must be
A) Equal
B) Proportional to frequency
C) Different
D) Zero
Q29: In a pie chart showing expenditure of a family, food takes 108°. The percentage spent on food is
A) 20%
B) 25%
C) 30%
D) 35%
Q30: Frequency polygon is closed by joining the first and last points to
A) Origin
B) Points with zero frequency on both sides
C) Mid-point of first class
D) X-axis directly
Q31: Bars in a bar graph are of
A) Equal width
B) Variable width
C) Width proportional to data
D) Any width
Q32: A pie chart is also known as
A) Circle graph
B) Sector graph
C) Both A and B
D) Angle graph
Q33: If one book symbol represents 200 books, then 3½ symbols represent
A) 400 books
B) 600 books
C) 700 books
D) 800 books
Q34: Double bar graph is used when we want to compare
A) One data set
B) Two data sets
C) Three data sets
D) More than three
Q35: In a histogram, the area of each rectangle represents
A) Frequency
B) Class width
C) Frequency density
D) Height
Q36: To represent the percentage of different crops grown in a village, the best graph is
A) Bar graph
B) Histogram
C) Pie chart
D) Frequency polygon
Q37: Frequency polygon can be drawn
A) With histogram only
B) Without histogram
C) Both ways
D) Only on X-axis
Q38: In a bar graph, the gaps between bars should be
A) Zero
B) Equal
C) Unequal
D) Very large
Q39: Central angle for 15% in a pie chart is
A) 36°
B) 45°
C) 54°
D) 72°
Q40: Which graph is most suitable for showing monthly temperature variation in a city?
A) Bar graph
B) Histogram
C) Frequency polygon
D) Pie chart
3. Reading and Interpreting Graphs (Q41–Q60)
Q41: In a bar graph, the height of a bar is 8 cm and the scale is 1 cm = 50 students. The actual number of students is
A) 50
B) 200
C) 400
D) 800
Q42: In a pictograph, one symbol represents 200 kg of wheat. If a village shows 4½ symbols, the total wheat produced is
A) 600 kg
B) 800 kg
C) 900 kg
D) 1000 kg
Q43: In a double bar graph showing boys and girls attendance, the taller bar for February indicates
A) More boys attended
B) More girls attended
C) Equal attendance
D) Cannot say without legend
Q44: In a histogram, the frequency of class 40–50 is 30 and width is 10. The height of the rectangle is
A) 3 units
B) 30 units
C) 300 units
D) Cannot determine
Q45: A pie chart shows 40% expenditure on education. The central angle for education is
A) 72°
B) 108°
C) 144°
D) 180°
Q46: In a frequency polygon, the highest peak corresponds to
A) Lowest frequency
B) Highest frequency
C) Median
D) Mean
Q47: From a bar graph, if the scale is 1 cm = 100 trees and a bar is 5.5 cm high, the number of trees planted is
A) 450
B) 500
C) 550
D) 600
Q48: In a pie chart of monthly budget, rent is 126°. The percentage spent on rent is
A) 30%
B) 35%
C) 40%
D) 45%
Q49: In a histogram with unequal class widths, the correct frequency is proportional to
A) Height of rectangle
B) Area of rectangle
C) Width only
D) Length of base
Q50: A double bar graph is given for production of rice and wheat in five years. Which year showed the maximum difference?
A) Requires calculation of difference each year
B) Year with tallest bar
C) Year with shortest bar
D) First year
Q51: In a pictograph, if one symbol = 50 books and a school shows 3 symbols + half symbol, total books are
A) 150
B) 175
C) 200
D) 225
Q52: The frequency polygon touches the x-axis at
A) Zero frequency points on both ends
B) Modal class
C) Median class
D) Never
Q53: From a pie chart, if transport sector is 54°, percentage share of transport is
A) 10%
B) 15%
C) 20%
D) 25%
Q54: In a histogram, two adjacent bars have no gap because the data is
A) Discrete
B) Continuous
C) Categorical
D) Random
Q55: Which information cannot be obtained from a bar graph?
A) Most frequent item
B) Exact difference
C) Total quantity
D) Trend over time
Q56: In a double bar graph, if the blue bar is always taller than the red bar, it means
A) Blue data is always greater
B) Red data is always greater
C) Equal every time
D) Cannot conclude without legend
Q57: A pie chart is unsuitable when
A) Showing parts of a whole
B) Comparing two years data
C) Total is 100%
D) Percentages are given
Q58: In a histogram, the class 20–30 has frequency 40 and next class 30–40 has frequency 25. The fall in frequency is
A) 10
B) 15
C) 25
D) 40
Q59: From a pictograph showing fruits sold, if mango = 5 symbols and one symbol = 20 kg, total mangoes sold are
A) 50 kg
B) 80 kg
C) 100 kg
D) 120 kg
Q60: In a frequency polygon, a sudden rise indicates
A) Decrease in frequency
B) Increase in frequency
C) No change
D) End of data
4. Measures of Central Tendency – Ungrouped Data (Q61–Q80)
Q61: The marks of 7 students are 45, 58, 45, 62, 70, 58, 45. The mode is
A) 45
B) 58
C) 62
D) Bimodal
Q62: For the data 12, 15, 18, 20, 22, the median is
A) 15
B) 18
C) 20
D) 22
Q63: Marks of 8 students: 34, 56, 45, 78, 56, 89, 67, 56. The mode is
A) 34
B) 56
C) 67
D) 89
Q64: The arithmetic mean of first five natural numbers is
A) 3
B) 4
C) 5
D) 6
Q65: For the data 10, 20, 30, 40, 50, 60 (6 observations), the median is
A) 30
B) 35
C) 40
D) 45
Q66: If the mean of 10 numbers is 25, the sum of the numbers is
A) 25
B) 100
C) 250
D) 350
Q67: In ungrouped data, if all values appear the same number of times, the data is
A) Bimodal
B) Trimodal
C) Multimodal
D) No mode
Q68: The most stable measure of central tendency is
A) Mean
B) Median
C) Mode
D) All equal
Q69: For the data 5, 8, 12, 15, 20, the mean is
A) 10
B) 12
C) 15
D) 60
Q70: Median is preferred over mean when data has
A) Extreme values
B) All values equal
C) No repetition
D) Only two values
Q71: If a student’s marks are 85, 90, 95, 70, 100, the median is
A) 85
B) 90
C) 95
D) 100
Q72: The mode of the data 3, 3, 5, 7, 8 is
A) 3
B) 5
C) 7
D) No mode
Q73: Mean of 9 numbers is 40. If one number 55 is removed, the mean of remaining 8 numbers is
A) 38
B) 38.125
C) 40
D) 45
Q74: For symmetric data, mean, median and mode are
A) Different
B) Equal
C) Mean > Median
D) Mode > Mean
Q75: The data 4, 7, 7, 9, 12, 12, 12, 15 has how many modes?
A) 1
B) 2
C) 3
D) No mode
Q76: Which measure is most affected by extreme values?
A) Mean
B) Median
C) Mode
D) All equally
Q77: The mean of 20 observations is 15. If each observation is multiplied by 2, new mean is
A) 15
B) 17
C) 30
D) 300
Q78: Mode is best used for
A) Average income
B) Most popular shoe size
C) House prices
D) Heights
Q79: For 11 players’ ages: 22, 25, 25, 27, 28, 30, 30, 30, 32, 35, 40, the median is
A) 28
B) 30
C) 32
D) 35
Q80: If mean = 50 and number of observations = 15, the sum of observations is
A) 65
B) 750
C) 765
D) 800
5. Measures of Central Tendency – Grouped Data (Q81–Q100)
Q81: The formula for arithmetic mean using assumed mean method is
A) x̄ = a + Σfᵢdᵢ / Σfᵢ
B) x̄ = a + h × Σfᵢuᵢ / Σfᵢ
C) x̄ = Σfᵢxᵢ / Σfᵢ
D) x̄ = a – Σfᵢdᵢ / Σfᵢ
Q82: The correct formula for median of grouped data is
A) l + [(N/2 – cf)/f] × h
B) l + [(N – cf)/f] × h
C) l + [N/2 / f] × h
D) l + (cf / f) × h
Q83: The empirical relationship between mean, median and mode is
A) Mode = 3 Median – 2 Mean
B) Mean = 3 Mode – 2 Median
C) Median = 3 Mean – 2 Mode
D) Mode = 2 Mean – 3 Median
Q84: Step-deviation method is most useful when
A) Deviations are large
B) Class width is large and uniform
C) Data is ungrouped
D) Frequency is zero
Q85: In grouped data, the class with maximum frequency is called
A) Median class
B) Modal class
C) Mean class
D) First class
Q86: The formula for mode is l + [(f₁ – f₀)/(2f₁ – f₀ – f₂)] × h. Here f₁ is
A) Frequency of class before modal class
B) Frequency of modal class
C) Frequency of class after modal class
D) Cumulative frequency
Q87: If mean = 48, median = 50, then mode (by empirical relation) ≈
A) 48
B) 50
C) 52
D) 54
Q88: In step-deviation method, h represents
A) Frequency
B) Class width
C) Assumed mean
D) Deviation
Q89: The median class is the class whose cumulative frequency is
A) Equal to N/2
B) Just greater than or equal to N/2
C) Just less than N/2
D) Maximum
Q90: Mean by direct method is always equal to mean by
A) Assumed mean method
B) Step-deviation method
C) Both A and B
D) Neither
Q91: If Σfᵢdᵢ = –120, Σfᵢ = 60, a = 50, then mean =
A) 48
B) 50
C) 52
D) 54
Q92: In the mode formula, f₀ and f₂ are frequencies of
A) Modal class and next class
B) Previous and next class of modal class
C) First and last class
D) Median class
Q93: If mean = 55, mode = 61, then median (empirical) ≈
A) 53
B) 57
C) 59
D) 61
Q94: Assumed mean should preferably be
A) A class mark near the middle
B) Zero
C) Maximum value
D) Minimum value
Q95: The mode formula is most accurate when the modal class has
A) Much higher frequency than adjacent classes
B) Equal frequency
C) Lower frequency
D) Zero frequency
Q96: In step-deviation, uᵢ =
A) (xᵢ – a)
B) (xᵢ – a)/h
C) xᵢ/h
D) (xᵢ + a)/h
Q97: If N = 120, the median lies in the class where cumulative frequency first exceeds
A) 60
B) 120
C) 30
D) 90
Q98: The mean obtained by any short-cut method should be
A) Different from direct method
B) Same as direct method
C) Greater
D) Smaller
Q99: If median = 45, mode = 51, then mean (empirical) ≈
A) 42
B) 43
C) 44
D) 45
Q99 (Corrected): If mode = 60 and median = 54, then mean ≈
A) 50
B) 51
C) 52
D) 53
Q100: Which method is also known as shortcut method?
A) Direct method
B) Assumed mean method
C) Median method
D) Mode method
6. Cumulative Frequency Distribution and Ogive (Q101–Q120)
Q101: The point of intersection of less-than ogive and more-than ogive gives
A) Mean
B) Median
C) Mode
D) Range
Q102: In a less-than ogive, points are plotted using
A) Lower limit and cumulative frequency
B) Upper limit and cumulative frequency
C) Class mark and frequency
D) Lower limit and frequency
Q103: More-than ogive is drawn by plotting
A) Upper limit vs ≥ cumulative frequency
B) Lower limit vs ≥ cumulative frequency
C) Upper limit vs ≤ cumulative frequency
D) Class mark vs cumulative frequency
Q104: Cumulative frequency of the first class in less-than type is always equal to
A) Zero
B) Frequency of first class
C) Total frequency N
D) Half of N
Q105: To find median from ogive, we draw a line from
A) (0, N/2) parallel to x-axis
B) (N/2, 0) parallel to y-axis
C) (N/2, N/2) to the curve
D) Any point on y-axis
Q106: The less-than ogive is
A) Increasing curve
B) Decreasing curve
C) Straight line
D) Parabola
Q107: The last point of more-than ogive lies at
A) (Lower limit of first class, N)
B) (Upper limit of last class, 0)
C) (Lower limit of first class, 0)
D) (Upper limit of last class, N)
Q108: If N = 80, the median from ogive is read at cumulative frequency
A) 40
B) 80
C) 20
D) 60
Q109: Ogives are generally drawn for
A) Ungrouped data
B) Grouped data
C) Discrete series only
D) Individual series
Q110: The more-than ogive starts from
A) Top-left
B) Bottom-left
C) Top-right
D) Bottom-right
Q111: Cumulative frequency of the last class in less-than ogive is
A) Zero
B) Frequency of last class
C) Total N
D) N/2
Q112: The shape of less-than ogive is generally
A) Concave upwards
B) Concave downwards
C) S-shaped
D) Straight line
Q113: The first point of less-than ogive is
A) (Upper limit of first class, frequency of first class)
B) (Lower limit of first class, 0)
C) (Upper limit of first class, 0)
D) (Lower limit of first class, frequency of first class)
Q114: Median from ogive is slightly different from formula method because
A) Graphical approximation
B) Wrong plotting
C) Different data
D) Error in calculation
Q115: The cumulative frequency table is constructed by
A) Adding frequencies downwards
B) Subtracting frequencies
C) Multiplying frequencies
D) Dividing frequencies
Q116: In more-than ogive, cumulative frequency decreases as
A) We move left
B) We move right
C) Value increases
D) Frequency increases
Q117: Ogive is another name for
A) Histogram
B) Frequency polygon
C) Cumulative frequency curve
D) Bar graph
Q118: To draw both ogives on the same graph, we need
A) One cumulative frequency table
B) Less-than and more-than cumulative frequencies
C) Only frequency table
D) Histogram
Q119: The median from ogive is found by
A) Highest point
B) Intersection point of two ogives
C) Lowest point
D) Mid-point of x-axis
Q120: Ogives can be used to find
A) Mean
B) Mode
C) Median and quartiles
D) Range only
7. Applications and Problem Solving (Q121–Q140)
Q121: The mean marks of 100 students is 58. Mean of first 65 students is 55. Mean of last 35 students is
A) 60
B) 61
C) 63
D) 64
Q122: If mean = 72, median = 70, then mode (empirical) ≈
A) 64
B) 66
C) 68
D) 70
Q123: In a frequency distribution, Σfᵢxᵢ = 4800, Σfᵢ = 120. The mean is
A) 30
B) 40
C) 50
D) 60
Q124: A student scored 15 runs above the team mean in 10 matches. If team mean is 45, his total runs are
A) 450
B) 500
C) 600
D) 650
Q125: In a pie chart, food expenditure is 126°. If total monthly income is ₹36,000, amount spent on food is
A) ₹10,000
B) ₹12,000
C) ₹12,600
D) ₹14,400
Q126: Mean of 50 families is ₹18,500. Later, one family with income ₹25,000 is added. New mean is
A) ₹18,600
B) ₹18,647
C) ₹18,686
D) ₹18,725
Q127: If median height of 80 students is 155 cm and from ogive it is 156 cm, the difference is due to
A) Calculation error
B) Graphical approximation
C) Wrong data
D) Different class interval
Q128: In a double bar graph, rainfall in July is 120 mm and 150 mm for two cities. The difference is
A) 20 mm
B) 30 mm
C) 40 mm
D) 50 mm
Q129: The mean of 8 numbers is 45. If one number is excluded, mean becomes 42. The excluded number is
A) 60
B) 63
C) 66
D) 69
Q129: Mean of 10 numbers is 48. After removing one number, mean of remaining 9 is 45. Removed number is
A) 66
B) 70
C) 72
D) 75
Q130: In a histogram, class 30–40 has frequency 50. If width is 10, area of rectangle is
A) 50
B) 500
C) 5
D) 40
Q131: If mean = 60, mode = 72, then median ≈
A) 64
B) 66
C) 68
D) 70
Q131: If mode = 75 and mean = 65, then median ≈
A) 68
B) 70
C) 72
D) 74
Q132: In a pictograph, one symbol = 400 votes. 5½ symbols mean
A) 2000
B) 2200
C) 2400
D) 2600
Q133: Mean rainfall of 12 months is 85 mm. Total annual rainfall is
A) 850 mm
B) 900 mm
C) 960 mm
D) 1020 mm
Q134: A shop sold 150, 200, 250, 300, 350 kg of rice in 5 days. The mean sale per day is
A) 240 kg
B) 250 kg
C) 260 kg
D) 300 kg
Q135: In a pie chart, education gets 72°. If total budget is ₹50,000, amount for education is
A) ₹8,000
B) ₹9,000
C) ₹10,000
D) ₹12,000
Q136: Mean of first 50 natural numbers is
A) 25
B) 25.5
C) 26
D) 50
Q137: If one student is added with marks 95 to a group whose mean is 75, new mean will
A) Decrease
B) Remain same
C) Increase
D) Become zero
Q138: In a histogram, frequency 60, class width 5, height of rectangle is
A) 10
B) 12
C) 15
D) 60
Q139: The average of 1, 3, 5, 7, 9 is
A) 4
B) 5
C) 6
D) 7
Q140: If mean = 55, median = 58, then mode ≈
A) 60
B) 62
C) 64
D) 66