Chapter 14: Statistics

VVI questions — the ones the board asked most (20)

1. Q1Short answer2 marksAsked: 2017, 2020, 2022

   Find the mean of the following distribution : | Class-interval | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | | --- | --- | --- | --- | --- | --- | | Frequency | 6 | 10 | 8 | 12 | 4 |

   

   Medha Ma’am

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   Watch it on the board · 25 s

   Model answer · Mean of grouped data, direct method

   1. 1.Class marks xᵢ: 30, 40, 50, 60, 70; fᵢxᵢ: 6 × 30 = 180, 10 × 40 = 400, 8 × 50 = 400, 12 × 60 = 720, 4 × 70 = 280.1 mark
   2. 2.Σfᵢ = 40 and Σfᵢxᵢ = 1980; mean x̄ = Σfᵢxᵢ / Σfᵢ = 1980/40 = 49.5.1 mark

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

2. Q2Long answer5 marksAsked: 2025

   Find the mean of the following distribution : [Table provided]

   

   Medha Ma’am

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   Model answer · mean of grouped data, direct method

   1. 1.The class mark (xi) of each class interval is obtained by taking the average of the upper and lower limits of that class, that is, xi = (upper limit + lower limit) / 2. Using this formula, the class mark xi is calculated for every class interval of the given distribution: for the first class xi = 5, for the second class xi = 15, for the third class xi = 25, for the fourth class xi = 35, and for the fifth class xi = 45, corresponding to the given frequencies fi = 7, 10, 15, 8, 10 respectively.1 mark
   2. 2.For each class interval, the product of the frequency (fi) and the class mark (xi) is found, that is, fi × xi is calculated for every class. For the given data, these products are obtained as: 7 × 5 = 35, 10 × 15 = 150, 15 × 25 = 375, 8 × 35 = 280, and 10 × 45 = 450. These values of fi xi are recorded in a separate column against the corresponding fi and xi for each class.1.5 marks
   3. 3.The sum of all the frequencies, Σfi, is obtained by adding all the fi values of the table: 7 + 10 + 15 + 8 + 10 = 50. The sum of all the products of frequency and class mark, Σfi xi, is obtained by adding all the fi xi values calculated for each class: 35 + 150 + 375 + 280 + 450 = 1290. Thus, Σfi = 50 and Σfi xi = 1290.1 mark
   4. 4.The mean of the given distribution is found using the formula: Mean = Σfi xi / Σfi, where Σfi xi is the sum of the products of frequency and class mark for all classes, and Σfi is the sum of all the frequencies.1 mark
   5. 5.Given: Σfi xi = 1290, Σfi = 50 Formula: Mean = Σfi xi / Σfi Substitution: Mean = 1290 / 50 Calculation: 1290 / 50 = 25.8 Answer: Mean = 25.80.5 marks

   • Write the formula exactly as 'Mean = Σfi xi / Σfi' before substituting the values.
   • Show the class mark formula xi = (upper limit + lower limit)/2 and compute it for every class, not just one.
   • Write the totals Σfi and Σfi xi clearly at the end of the table before substituting them in the formula, and end with the final numerical value of the mean with no unit missing.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

3. Q3Long answer5 marksAsked: 2025

   Find the mean of the following distribution : Class-interval 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Frequency 7 6 9 13 20 5 4

   

   Medha Ma’am

   AskMedha’s AI teacher

   Hear it from Medha Ma’am · 175 s

   Model answer · mean of grouped data, direct method

   1. 1.The class mark (xi) of each class interval is found by taking the average of its upper and lower limits, that is, Class mark = (Upper class limit + Lower class limit)/2. For the class interval 11-13, the class mark is (11+13)/2 = 12. Similarly, for 13-15, 15-17, 17-19, 19-21, 21-23, 23-25, the class marks come out to be 14, 16, 18, 20, 22, 24 respectively.1 mark
   2. 2.The product of each class mark (xi) and its corresponding frequency (fi) is obtained as fi xi. For the class intervals, multiplying frequency with its class mark: 7 × 12 = 84, 6 × 14 = 84, 9 × 16 = 144, 13 × 18 = 234, 20 × 20 = 400, 5 × 22 = 110, 4 × 24 = 96. Thus the products fi xi are 84, 84, 144, 234, 400, 110, 96 respectively.1.5 marks
   3. 3.The sum of all frequencies is Σfi = 7 + 6 + 9 + 13 + 20 + 5 + 4 = 64. The sum of all the products fi xi is Σfi xi = 84 + 84 + 144 + 234 + 400 + 110 + 96 = 1152.1 mark
   4. 4.The mean of grouped data by the direct method is given by the formula: x̄ = Σfi xi / Σfi, where fi xi is the product of frequency and class mark of each class interval, and Σfi is the sum of all the frequencies.0.5 marks
   5. 5.Substituting the values Σfi xi = 1152 and Σfi = 64 in the formula x̄ = Σfi xi / Σfi, we get x̄ = 1152/64 = 18. Therefore, the mean of the given distribution is 18.1 mark

   • Make a table with columns for class interval, frequency (fi), class mark (xi) and the product fi xi, and show the working inside it.
   • Write the formula x̄ = Σfi xi / Σfi before substituting values.
   • End with the final answer stated as 'the mean of the given distribution is 18' with no unit needed.

   Marks split from a structure derived from past papers (checked twice); not Bihar Board’s official scheme

4. Q4Long answer5 marksAsked: 2025

   Find the mean of the following distribution : | Class-interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 | | --- | --- | --- | --- | --- | --- | --- | --- | | Frequency | 7 | 6 | 9 | 13 | 20 | 5 | 4 |

   How the model answer begins

   1. Class marks (x): 12, 14, 16, 18, 20, 22, 24 (frequencies f: 7, 6, 9, 13, 20, 5, 4).

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5. Q5Long answer5 marksAsked: 2026

   Find the median of the following data : | Marks obtained | less than 10 | less than 20 | less than 30 | less than 40 | less than 50 | less than 60 | less than 70 | less than 80 | less than 90 | less than 100 | | No. of students | 5 | 8 | 12 | 15 | 18 | 22 | 29 | 38 | 45 | 53 |

   How the model answer begins

   1. From the 'less than' cumulative frequencies, the class intervals and frequencies are: 0-10: 5, 10-20: 8 − 5 = 3, 20-30: 4, 30-40: 3, 40-50: 3, 50-60: 4, 60-70: 7, 70-80: 9, 80-90: 7, 90-100: 8.

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6. Q6Long answer5 marksAsked: 2026

   Find the median of the following distribution : Class interval 118-126 127-135 136-144 145-153 154-162 163-171 172-180 Frequency 3 5 9 12 5 4 2

   How the model answer begins

   1. Since the given class intervals are not continuous, they are converted to continuous classes by subtracting 0.5 from each lower limit and adding 0.5 to each upper limit. The classes 118-126, 127-135, 136-144, 145-153,…

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7. Q7Long answer5 marksAsked: 2022

   Find the mode of the following distribution : Class-interval 0-20, 20-40, 40-60, 60-80, 80-100, 100-120. Frequency 10, 35, 52, 61, 38, 29.

   How the model answer begins

   1. The maximum frequency is 61, which lies in the class interval 60-80. So, the modal class is 60-80. Therefore, the lower limit (l) of the modal class = 60, the class size (h) = 20, the frequency (f1) of modal class = 61,…

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8. Q8Long answer5 marksAsked: 2022

   The mean of the given data is 18. Then find the unknown frequency: Class-interval: 11-13, 13-15, 15-17, 17-19, 19-21, 21-23, 23-25. No. of children: 7, 6, 9, 13, f, 5, 4.

   How the model answer begins

   1. The mid-point (or class mark) of each class is found by finding the average of its upper and lower limits, that is, Class mark = (Upper class limit + Lower class limit)/2. For the given class intervals 11-13, 13-15,…

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9. Q9Long answer5 marksAsked: 2022

   Find the mode of the following distribution : Class-interval 0-10, 10-20, 20-30, 30-40, 40-50; Frequency 14, 23, 27, 21, 15

   How the model answer begins

   1. The maximum frequency among the given classes is 27, which lies in the class 20-30. So the modal class is 20-30. The lower limit (l) of the modal class = 20, the class size (h) = 10, the frequency (f1) of the modal…

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10. Q10Long answer5 marksAsked: 2023

    Find the mean of the following distribution : Class-interval 5-15, 15-25, 25-35, 35-45, 45-55, 55-65; Frequency 6, 11, 21, 23, 14, 5.

    How the model answer begins

    1. Class marks xᵢ = (lower limit + upper limit)/2: 10, 20, 30, 40, 50, 60.

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11. Q11Long answer5 marksAsked: 2022

    Find the mode of the following distribution: | Class-interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | --- | --- | --- | --- | --- | --- | | Frequency | 14 | 23 | 27 | 21 | 15 |

    How the model answer begins

    1. The maximum frequency is 27, in the class 20–30, so the modal class is 20–30.

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12. Q12Long answer5 marksAsked: 2023

    Find the mean of the following distribution: | Class-interval | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | | --- | --- | --- | --- | --- | --- | --- | | Frequency | 6 | 11 | 21 | 23 | 14 | 5 |

    How the model answer begins

    1. Class marks xᵢ: 10, 20, 30, 40, 50, 60.

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13. Q13Long answer5 marksAsked: 2022

    The mean of the given data is 18. | Class-Interval | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 | | --- | --- | --- | --- | --- | --- | --- | --- | | No. of children | 7 | 6 | 9 | 13 | f | 5 | 4 | Then find the unknown frequency:

    How the model answer begins

    1. Class marks xᵢ = 12, 14, 16, 18, 20, 22, 24.

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14. Q14Short answer2 marksAsked: 2026

    Find the mean of first 10 prime numbers.

    How the model answer begins

    1. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Adding these numbers, we get 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129. So the sum of the first 10 prime numbers is 129.

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15. Q15Short answer2 marksAsked: 2023

    Find the mean of the following data : Marks obtained 10 15 20 25 30 Number of students 4 6 3 2 5

    How the model answer begins

    1. For the given data, marks obtained (xi) are 10, 15, 20, 25, 30 with corresponding number of students (fi) as 4, 6, 3, 2, 5. We find fixi for each value: for xi = 10, fixi = 10 × 4 = 40; for xi = 15, fixi = 15 × 6 = 90;…

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16. Q16Short answer2 marksAsked: 2022

    Find the mean of the following distribution : Class-interval 0-100 100-200 200-300 300-400 400-500 Frequency 6 9 15 12 8

    How the model answer begins

    1. The class marks (xi) of each class interval are found by Class mark = (Upper class limit + Lower class limit)/2. For 0-100, xi = (0+100)/2 = 50 For 100-200, xi = (100+200)/2 = 150 For 200-300, xi = (200+300)/2 = 250 For…

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17. Q17Short answer2 marksAsked: 2023

    Find the mean of the following data : | Marks obtained | 10 | 15 | 20 | 25 | 30 | | --- | --- | --- | --- | --- | --- | | Number of students | 4 | 6 | 3 | 2 | 5 |

    How the model answer begins

    1. Mean = Σfx / Σf.

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18. Q18Short answer2 marksAsked: 2021

    Find the mean of the following distribution : | Class interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | --- | --- | --- | --- | --- | --- | | Frequency | 20 | 24 | 40 | 36 | 20 |

    How the model answer begins

    1. Class marks xᵢ = 5, 15, 25, 35, 45; fᵢxᵢ = 20 × 5 = 100, 24 × 15 = 360, 40 × 25 = 1000, 36 × 35 = 1260, 20 × 45 = 900; Σfᵢ = 140 and Σfᵢxᵢ = 3620.

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19. Q19Short answer2 marksAsked: 2021

    Find the mode of the following distribution : Class-interval: 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 Frequency: 7 | 17 | 32 | 10 | 4 | 2

    How the model answer begins

    1. The maximum class frequency is 32, and the class corresponding to this frequency is 20-30. So, the modal class is 20-30, with lower limit (l) = 20, class size (h) = 10, frequency (f1) of the modal class = 32, frequency…

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20. Q20Short answer2 marksAsked: 2021

    Find the mean of the following distribution : Class-interval: 0-10 | 10-20 | 20-30 | 30-40 | 40-50 Frequency: 6 | 9 | 8 | 13 | 20

    How the model answer begins

    1. Class mark = (Upper class limit + Lower class limit)/2. For the classes 0-10, 10-20, 20-30, 30-40, 40-50, the class marks xi are 5, 15, 25, 35, 45.

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1 more questions of this chapter, each with its model answer, in the AskMedha app.

Objective questions with the board’s key (10)

1. 1. Bihar Board 2026

   Cumulative frequency table is required for the calculation of which of the following measures of central tendency ?

   • (A) Mean
   • (B) Median ✓
   • (C) Mode
   • (D) None of these

   Answer: (B)

2. 2. Bihar Board 2026

   Median of the first 10 prime numbers is

   • (A) 11
   • (B) 12 ✓
   • (C) 13
   • (D) 17

   Answer: (B)

3. 3. Bihar Board 2026

   In symmetrical frequency distribution table it holds

   • (A) Mean > Mode > Median
   • (B) Mean < Mode < Median
   • (C) Mean = Mode = Median ✓
   • (D) Mode = (Mean + Median) / 2

   Answer: (C)

4. 4. Bihar Board 2026

   If the mean and mode of a frequency distribution are 28 and 16 respectively then median is

   • (A) 22
   • (B) 23
   • (C) 24 ✓
   • (D) 25

   Answer: (C)

5. 5. Bihar Board 2026

   The average of 24 numbers is zero. Out of them maximum how many numbers may be greater than zero ?

   • (A) 0
   • (B) 1
   • (C) 12
   • (D) 23 ✓

   Answer: (D)

6. 6. Bihar Board 2026

   Which of the following is not a measure of central tendency?

   • (A) Mean
   • (B) Median
   • (C) Mode
   • (D) Standard deviation ✓

   Answer: (D)

7. 7. Bihar Board 2026

   If the mean of 6, 8, 9, x and 13 is 10, then the value of x is

   • (A) 12
   • (B) 14 ✓
   • (C) 16
   • (D) 18

   Answer: (B)

8. 8. Bihar Board 2026

   The median of 15, 6, 16, 8, 22, 21, 9, 18, 25 is

   • (A) 15
   • (B) 18
   • (C) 16 ✓
   • (D) 22

   Answer: (C)

9. 9. Bihar Board 2026

   The arithmetic mean of a and b is

   • (A) ab/2
   • (B) (a+b)/2 ✓
   • (C) (a-b)/2
   • (D) sqrt(ab)

   Answer: (B)

10. 10. Bihar Board 2026

    The mode of 2, 6, 4, 5, 0, 1, 3, 2 is

    • (A) 1
    • (B) 2 ✓
    • (C) 3
    • (D) 4

    Answer: (B)

Questions parents and students ask

How many marks does "Statistics" carry in Bihar Board Class 10 Maths?

In the Bihar Board papers of 2021–2026, this chapter carried about 6 marks and about 7 questions a year; by marks it ranks 9 in Maths.

Which are the most important (VVI) questions of "Statistics"?

The 20 questions above are from the board’s real papers, each with the years it was asked; the most-asked come first with their full model answers. All 21 written questions of this chapter, with answers, are in the AskMedha app.

Do the answers follow the board’s marking scheme?

BSEB does not publish a marking scheme. Each answer is written point by point on a structure derived from past papers and checked by a second, independent model; it is never called the board’s official scheme.