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 Q26. Find the median of the following frequency distribution: Class: $140\text{–}145, 145\text{–}150, 150\text{–}155, 155\text{–}160, 160\text{–}165$ Frequency: $5, 15, 30, 15, 5$
- 3 Marks Q27. Calculate the median marks for the distribution: Marks: $20, 70, 50, 60, 75, 90, 40$ Students: $8, 12, 18, 6, 9, 5, 12$
- 3 Marks Q28. Convert the following "less than type" cumulative frequency distribution into a standard grouped frequency table: Below 10 (3), Below 20 (12), Below 30 (27), Below 40 (57), Below 50 (75).
- 3 Marks Q29. Find the median for the data showing weekly expenses of households: Expenses (₹): $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50$ Households: $8, 15, 20, 12, 5$
- 3 Marks Q30. Calculate the median height from the distribution of saplings: Height (cm): $10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50, 50\text{–}60$ Frequency: $4, 8, 14, 10, 4$
- 3 Marks Q31. Find the median for the following discrete frequency series: $x$: $5, 6, 7, 8, 9, 10, 11$ $f$: $4, 7, 12, 18, 11, 6, 2$
- 3 Marks Q32. Find the lower limit of the median class for the data: Class: $0\text{–}5, 5\text{–}10, 10\text{–}15, 15\text{–}20, 20\text{–}25$ Frequency: $10, 15, 25, 20, 10$
- 3 Marks Q33. Find the upper limit of the median class for the following distribution: Class: $100\text{–}120, 120\text{–}140, 140\text{–}160, 160\text{–}180, 180\text{–}200$ Frequency: $10, 20, 35, 15, 5$
- 3 Marks Q34. Compute the median score of 50 students: Score: $20\text{–}30, 30\text{–}40, 40\text{–}50, 50\text{–}65, 65\text{–}80$ Students: $6, 9, 18, 12, 5$
- 3 Marks Q35. Find the median length of 40 plant leaves measured to the nearest millimeter.
- 3 Marks Q36. Construct cumulative frequency curves to locate the median value graphically for a standard frequency distribution with $N = 60$
- 3 Marks Q37. Find the median for data where $N = 100$, lower limit $l = 40$, $cf = 36$, $f = 20$, and class size $h = 10$.
- 3 Marks Q38. Explain why cumulative frequencies are essential for calculating the median of grouped data.
- 3 Marks Q39. Find the mode of the following grouped frequency distribution: Class: $10\text{–}15, 15\text{–}20, 20\text{–}25, 25\text{–}30, 30\text{–}35$ Frequency: $3, 8, 12, 10, 5$
- 3 Marks Q40. Calculate the mode for the marks distribution: Marks: $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50, 50\text{–}60$ Frequency: $5, 10, 18, 30, 20, 7$
- 3 Marks Q41. Find the mode of the wickets taken by a bowler in matches: $2, 6, 4, 5, 0, 2, 1, 3, 2, 3$
- 3 Marks Q42. Calculate the mode of shoe sizes sold in a store: Size: $4, 5, 6, 7, 8, 9, 10$ Pairs: $1, 4, 3, 20, 45, 25, 2$
- 3 Marks Q43. If the median of a distribution is $24$ and mean is $24.5$, find its mode using the empirical relationship.
- 3 Marks Q44. Given that the mode and mean of a dataset are $30$ and $25$ respectively, find its median.
- 3 Marks Q45. If the value of mean and mode are respectively $30$ and $15$, find the median.
- 3 Marks Q46. Find the mode of the following distribution of daily profits of shops: Profit (₹): $0\text{–}10, 10\text{–}20, 20\text{–}30, 30\text{–}40, 40\text{–}50$ Shops: $7, 18, 32, 20, 6$
- 3 Marks Q47. Find the sum of the lower limit of the modal class and the upper limit of the median class for a given standard frequency setup.
- 3 Marks Q48. Explain the empirical relationship connecting mean, median, and mode, and state where it fails.
- 3 Marks Q49. Calculate the mode of the following continuous frequency table: Class: $20\text{–}30, 30\text{–}40, 40\text{–}50, 50\text{–}60, 60\text{–}70$ Frequency: $10, 28, 30, 14, 8$
- 3 Marks Q50. Find the modal class and compute the mode for a data set representing computer operating hours: Hours: $0\text{–}5, 5\text{–}10, 10\text{–}15, 15\text{–}20$ Frequency: $2, 8, 22, 10$
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