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 E — Long Answer Type Questions [5 Marks Each]
- 5 Marks Q1. The following table shows the daily pocket allowance of children in a locality. The mean pocket allowance is ₹ 18. Find the missing frequency $f$: Class ($₹$): $11-13,\ 13-15,\ 15-17,\ 17-19,\ 19-21,\ 21-23,\ 23-25$ Frequency: $3,\ 6,\ 9,\ 13,\ f,\ 5,\ 4$
- 5 Marks Q2. Compute the mean daily wages of 50 workers in a factory using an appropriate shortcut method (such as step-deviation): Daily Wages ($₹$): $100-120,\ 120-140,\ 140-160,\ 160-180,\ 180-200$ Number of Workers: $12,\ 14,\ 8,\ 6,\ 10$
- 5 Marks Q3. Thirty women were examined in a hospital, and the number of heartbeats per minute was recorded. Find the mean heartbeats per minute using the step-deviation or assumed mean method: Heartbeats/min: $65-68,\ 68-71,\ 71-74,\ 74-77,\ 77-80,\ 80-83,\ 83-86$ No. of Women: $2,\ 4,\ 3,\ 8,\ 7,\ 4,\ 2$
- 5 Marks Q4. The distribution below gives the weights of 30 students of a class. Find the median weight of the students along with a complete step-by-step table. Weight (in kg): $40-45,\ 45-50,\ 50-55,\ 55-60,\ 60-65,\ 65-70,\ 70-75$ Number of Students: $2,\ 3,\ 8,\ 6,\ 6,\ 3,\ 2$
- 5 Marks Q5. Find the mean, median, and mode for the following continuous frequency distribution and verify the empirical relationship among them: Class: $0-10,\ 10-20,\ 20-30,\ 30-40,\ 40-50,\ 50-60,\ 60-70$ Frequency: $5,\ 8,\ 15,\ 20,\ 14,\ 8,\ 5$
- 5 Marks Q6. The arithmetic mean of the following frequency distribution is 53. If the total frequency is 100, find the missing frequencies $f_1$ and $f_2$: Class: $0-20,\ 20-40,\ 40-60,\ 60-80,\ 80-100$ Frequency: $15,\ f_1,\ 37,\ f_2,\ 10$
- 5 Marks Q7. If the median of the distribution given below is 525 and the total frequency is 100, find the values of missing frequencies $x$ and $y$: Class: $0-100,\ 100-200,\ 200-300,\ 300-400,\ 400-500,\ 500-600,\ 600-700,\ 700-800,\ 800-900,\ 900-1000$ Frequency: $2,\ 5,\ x,\ 12,\ 17,\ 20,\ y,\ 9,\ 7,\ 4$
- 5 Marks Q8. The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Find the missing frequencies $f_1$ and $f_2$: Class: $0-20,\ 20-40,\ 40-60,\ 60-80,\ 80-100,\ 100-120$ Frequency: $5,\ f_1,\ 10,\ f_2,\ 7,\ 8$
- 5 Marks Q9. Given that the median of 60 observations is 28.5, find the values of missing frequencies $x$ and $y$: Class: $0-10,\ 10-20,\ 20-30,\ 30-40,\ 40-50,\ 50-60$ Frequency: $5,\ x,\ 20,\ 15,\ y,\ 5$
- 5 Marks Q10. The monthly expenditure on milk in 200 families of a housing society is given below. Find the missing frequencies corresponding to the median class range and compute the overall mean expenditure: Expenditure ($₹$): $1000-1500,\ 1500-2000,\ 2000-2500,\ 2500-3000,\ 3000-3500,\ 3500-4000,\ 4000-4500,\ 4500-5000$ Frequency: $24,\ 40,\ p,\ 33,\ q,\ 30,\ 22,\ 16$ (given total families = 200)
- 5 Marks Q11. Find the mode of the following data representing the lifetime (in hours) of 225 electrical components: Lifetime (hrs): $0-20,\ 20-40,\ 40-60,\ 60-80,\ 80-100,\ 100-120$ Frequency: $10,\ 35,\ 52,\ 61,\ 38,\ 29$
- 5 Marks Q12. The data regarding the heights of 50 girls of a class was tabulated. Calculate the median and modal heights, and check how close they are: Height (in cm): $120-130,\ 130-140,\ 140-150,\ 150-160,\ 160-170$ Number of Girls: $2,\ 8,\ 12,\ 20,\ 8$
- 5 Marks Q13. A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members. Find the mode and mean of the data: Family Size: $1-3,\ 3-5,\ 5-7,\ 7-9,\ 9-11$ Number of Households: $7,\ 8,\ 2,\ 2,\ 1$
- 5 Marks Q14. Find the missing frequency $f$ and the median of the distribution given that the mode is $34.5$ and the modal class is $30-40$: Class: $10-20\ (5),\ 20-30\ (9),\ 30-40\ (12),\ 40-50\ (f),\ 50-60\ (3)$
- 5 Marks Q15. The profits (in lakhs ₹) of 100 shops in a commercial market distribution are recorded below. Find the median and modal profit values: Profit: $0-5,\ 5-10,\ 10-15,\ 15-20,\ 20-25$ Number of Shops: $10,\ 22,\ 35,\ 21,\ 12$
- 5 Marks Q16. The annual profits earned by 30 shops in a shopping complex give the following distribution. Draw both a "less than type" and a "more than type" ogive on the same graph paper, and determine the median profit from the intersection point: Profit (in lakhs): More than or equal to $5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35$ Cumulative Frequency: $30,\ 28,\ 16,\ 14,\ 10,\ 7,\ 3$
- 5 Marks Q17. During a medical check-up of 35 students of a class, their weights were recorded as follows. Draw a "less than type" ogive for the data, and use it to find the median weight: Weight (in kg): Less than $38,\ 40,\ 42,\ 44,\ 46,\ 48,\ 50,\ 52$ Number of Students: $0,\ 3,\ 5,\ 9,\ 14,\ 28,\ 32,\ 35$
- 5 Marks Q18. A student notes down the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarizes it in the table below. Find the median and mode of the data: No. of Cars: $0-10,\ 10-20,\ 20-30,\ 30-40,\ 40-50,\ 50-60,\ 60-70,\ 70-80$ Frequency: $7,\ 14,\ 13,\ 12,\ 20,\ 11,\ 15,\ 8$
- 5 Marks Q19. The median of the following data is $525$. If the total frequency is $100$ and the class interval size is uniform ( $h=100$), construct the full cumulative table layout, solve for the unknown partitions, and explain how the median class is identified.
- 5 Marks Q20. A test is conducted for 100 applicants. The scores are classified into intervals of width $10$ starting from $0$. If the mean score is evaluated as $54.5$ and the sum of frequencies of the extreme ends ($0-10$ and $90-100$) totals $8$, establish the full distribution table layout showing step-by-step evaluation for missing boundaries
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