CBSE 2024 Board Practice Questions
Q1. Empirical relationship between the three measures of central tendency is:
(A) 3 Median = Mode + 2 Mean (B) 2 Median = Mode + 3 Mean
(C) 3 Mean = Mode + 2 Median (D) Mean = Mode + Median
Q2. If the mean of a frequency distribution is 25 and the mode is 25, then its median is:
(A) 25 (B) 50 (C) 12.5 (D) 0
Q3. The mode of a grouped frequency distribution is 65. If the modal class is 60–80 with f₁ = 12, f₀ = 8, f₂ = x, and h = 20, find x.
Q4. Find the mean of the following distribution using Assumed Mean Method:
Classes: 0–10, 10–20, 20–30, 30–40, 40–50
Frequencies: 7, 10, 15, 8, 10
Q5. If the median of the following frequency distribution is 28.5, find the values of missing frequencies x and y (Total Frequency N = 60):
Class Interval: 0–10 (5), 10–20 (x), 20–30 (20), 30–40 (15), 40–50 (y), 50–60 (5)
CBSE 2023 Board Practice Questions
Q6. While computing mean of grouped data, we assume that the frequencies are:
(A) evenly distributed over all the classes
(B) centered at the class marks of the classes
(C) centered at the upper limits
(D) centered at the lower limits
Q7. Find the mode of the following frequency distribution:
Class: 0–20 (6), 20–40 (8), 40–60 (10), 60–80 (7), 80–100 (4)
Q8. Find the median of the following distribution:
Marks: 0–10 (5), 10–20 (8), 20–30 (20), 30–40 (12), 40–50 (5)
Q9. The mean of the following distribution is 53. Find the missing frequencies f₁ and f₂ if total frequency is 100:
Class: 0–20 (15), 20–40 (f₁), 40–60 (21), 60–80 (f₂), 80–100 (17)
CBSE 2022 Board Practice Questions
Q10. Find the upper limit of the modal class of the distribution:
Class: 0–5 (10), 5–10 (15), 10–15 (12), 15–20 (20), 20–25 (9)
Q11. For the following distribution, find the modal class and its frequency:
Marks: 10–20 (3), 20–30 (12), 30–40 (20), 40–50 (15), 50–60 (5)
Q12. Find the mean of the following data using Direct Method:
Class: 10–25 (2), 25–40 (3), 40–55 (7), 55–70 (6), 70–85 (6), 85–100 (6)
CBSE 2021 Board Practice Questions
Q13. If the mode of a data is 18 and mean is 24, find its median using empirical formula.
Q14. Find the class mark of the modal class for the following frequency distribution:
Class: 1–3 (7), 3–5 (8), 5–7 (2), 7–9 (2), 9–11 (1)
Q15. Calculate the median for the following grouped frequency distribution:
Class: 135–140 (4), 140–145 (11), 145–150 (29), 150–155 (40), 155–160 (6)
CBSE 2020 Board Practice Questions
Q16. Construction of a cumulative frequency table is useful in determining the:
(A) Mean (B) Median (C) Mode (D) All three
Q17. Find the mode of the following data:
Class: 10–20 (4), 20–30 (8), 30–40 (10), 40–50 (12), 50–60 (10), 60–70 (4), 70–80 (2)
Q18. The mean of the following frequency distribution is 50. Find the values of p and q if total frequency is 120:
Class: 0–20 (17), 20–40 (p), 40–60 (32), 60–80 (q), 80–100 (19)
Tips for Solving Board PYQs
Use the empirical formula 3 Median = Mode + 2 Mean for 1-mark numericals.
Always calculate N / 2 first to identify the median class in cumulative frequency tables.
For missing frequency problems, use two equations: Sum of frequencies = Total N and the Mean/Median formula.