Internal Assessment / Mathematics Test
Statistics & Probability
Time Allowed: 30 Minutes
Maximum Marks: 05
Q.
If the median of the distribution given below is 525 and the total frequency is 100, find the values of the missing frequencies x and y.
[5 Marks]
| Class Interval | Frequency |
|---|---|
| 0 - 100 | 2 |
| 100 - 200 | 5 |
| 200 - 300 | x |
| 300 - 400 | 12 |
| 400 - 500 | 17 |
| 500 - 600 | 20 |
| 600 - 700 | y |
| 700 - 800 | 9 |
| 800 - 900 | 7 |
| 900 - 1000 | 4 |
| Total |
SECTION C — Short Answer Type Questions [3 Marks Each]
- 3 Marks Q1. Find the mean of the following frequency distribution using the direct method: Class: $10\text{–}25, 25\text{–}40, 40\text{–}55, 55\text{–}70, 70\text{–}85, 85\text{–}100$ Frequency: $2, 3, 7, 6, 6, 6$
- 3 Marks Q2. Calculate the mean daily wages of workers using the assumed-mean method ($a = 550$): Wages (₹): $500\text{–}520, 520\text{–}540, 540\text{–}560, 560\text{–}580, 580\text{–}600$ Workers: $12, 14, 8, 6, 10$
- 3 Marks Q3. Find the mean of the following data using the step-deviation method: Class: $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50$ Frequency: $7, 10, 15, 8, 10$
- 3 Marks Q4. The mean of the following distribution is $18$. Find the frequency $f$ of the class $19\text{–}21$: Class: $11\text{–}13, 13\text{–}15, 15\text{–}17, 17\text{–}19, 19\text{–}21, 21\text{–}23, 23\text{–}25$ Frequency: $3, 6, 9, 13, f, 5, 4$
- 3 Marks Q5. Calculate the mean marks obtained by 100 students: Marks: $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50$ Students: $12, 23, 34, 25, 6$
- 3 Marks Q6. Find the mean of the following frequency distribution: Class: $0\text{–}15, 15\text{–}30, 30\text{–}45, 45\text{–}60, 60\text{–}75, 75\text{–}90$ Frequency: $17, 20, 18, 21, 15, 9$
- 3 Marks Q7. If the mean of the following distribution is $7.5$, find the value of $p$: $x$: $3, 5, 7, 9, 11, 13$ $f$: $6, 8, 15, p, 8, 4$
- 3 Marks Q8. Find the mean of the first 10 natural numbers using direct statistical approaches for discrete data.
- 3 Marks Q9. The arithmetic mean of the following table is $50$. Find the missing frequencies $p$ and $q$ given that total frequency is $120$: Class: $0\text{–}20, 20\text{–}40, 40\text{–}60, 60\text{–}80, 80\text{–}100$ Frequency: $17, p, 32, q, 19$
- 3 Marks Q10. Find the mean weight of 30 packet samples where weights are grouped as: Weight (g): $40\text{–}45, 45\text{–}50, 50\text{–}55, 55\text{–}60, 60\text{–}65$ Packets: $2, 3, 8, 12, 5$
- 3 Marks Q11. Determine the average score of a cricket team across matches given: Runs: $0\text{–}20, 20\text{–}40, 40\text{–}60, 60\text{–}80, 80\text{–}100$ Matches: $4, 6, 12, 10, 8$
- 3 Marks Q12. If each observation in a raw dataset is increased by $5$, how does the overall mean change? Prove it theoretically for a small sample of 5 items
- 3 Marks Q13. Find missing frequencies $x$ and $y$ if total frequency is $100$ and median is $525$: Class: $0\text{–}100, 100\text{–}200, 200\text{–}300, 300\text{–}400, 400\text{–}500, 500\text{–}600, 600\text{–}700, 700\text{–}800, 800\text{–}900, 900\text{–}1000$ Frequency: $2, 5, x, 12, 17, 20, y, 9, 7, 4$
- 3 Marks Q14. Find missing frequencies $f_1$ and $f_2$ in the distribution given below, where total frequency is $50$ and median is $28.5$: Class: $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50, 50\text{–}60$ Frequency: $5, f_1, 20, 15, f_2, 5$
- 3 Marks Q15. The sum of all frequencies in a grouped frequency table is $60$. Median class is $30\text{–}40$, cumulative frequency before it is $22$, frequency of median class is $12$, and class size is $10$. Find the median.
- 3 Marks Q16. Find the missing frequency $p$ given that the total frequency is $100$ and mean is $50$: Class: $20\text{–}40, 40\text{–}60, 60\text{–}80, 80\text{–}100$ Frequency: $25, p, 30, 20$ (adjust boundary conditions accordingly)
- 3 Marks Q17. If $\sum f_i = 15$, $\sum f_i x_i = 3p + 36$, and the mean of the distribution is $3$, find $p$.
- 3 Marks Q18. Find $k$ if the mean of observations $2, 4, 6, 8, 10, k$ is $7$.
- 3 Marks Q19. Given $\sum f_i = 17$, $\sum f_i x_i = 4P + 63$, and mean $= 7$, find the value of $P$.
- 3 Marks Q20. In a distribution, if $\sum f_i = 20$, mean $= 12$, and $\sum f_i x_i = 150 + k$, find $k$.
- 3 Marks Q21. Find the missing value $x$ if the mode of data $4, 5, 6, 8, 5, 4, 8, 5, 6, x, 8$ is $8$.
- 3 Marks Q22. If the median of numbers $5, 7, 10, 12, 2x-8, 2x+10, 35, 41, 42, 50$ (arranged in ascending order) is $25$, find $x$.
- 3 Marks Q23. Find the missing frequency $f$ when the total frequency is $30$ for: $x$: $10, 20, 30, 40, 50$ $f$: $3, f, 6, 10, 5$
- 3 Marks Q24. Determine the value of $m$ if the mean of the following series is $15$: $x$: $5, 10, 15, 20, 25$ $f$: $6, m, 6, 10, 4$
- 3 Marks Q25. Find missing $a$ given that mode is $36$ for a distribution where modal class interval frequency parameters are balanced.
Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :
English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
Copyright © 2026 Deepa Maths Academy | Global Examination & Academic Portal. All Rights Reserved.