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 B — Very Short Answer Type Questions [2 Marks Each]
- 2 Marks Q26. If a "less than" ogive is drawn, which values are plotted along the $x$-axis?
- 2 Marks Q27. The median of a distribution is given as $32$. If $N=50$, what is the cumulative frequency corresponding to the median position?
- 2 Marks Q28. Given a distribution with cumulative frequencies $4, 9, 18, 30, 45$, find the frequency of the 4th class interval ($30-40$ range).
- 2 Marks Q29. What is the sum of the lower limits of the median class and modal class for the distribution: $0-10$ (2), $10-20$ (5), $20-30$ (12), $30-40$ (8)?
- 2 Marks Q30. How does changing raw data into continuous class intervals affect the calculation of the median?
- 2 Marks Q31. Write the formula for calculating the mode of a grouped data and define $f_1, f_0,$ and $f_2$.
- 2 Marks Q32. Find the mode of the data: $5, 7, 8, 5, 6, 9, 5, 10$.
- 2 Marks Q33. Can the mode of a distribution be a value outside the given data range? Explain.
- 2 Marks Q34. Find the modal class for the following distribution: Class: $10-20,\ 20-30,\ 30-40,\ 40-50$ Frequency: $4,\ 12,\ 9,\ 5$
- 2 Marks Q35. If the mode of a data is $24$ and the mean is $27$, find its median.
- 2 Marks Q36. Find the missing frequency $x$ if the median of the distribution is $35$: Class: $0-10\ (2),\ 10-20\ (3),\ 20-30\ (x),\ 30-40\ (6),\ 40-50\ (5)$
- 2 Marks Q37. Why is the empirical formula (Mode = $3$ Median $- 2$ Mean) particularly useful in moderately skewed distributions?
- 2 Marks Q38. Give an example of a situation where the mode is a more appropriate measure of central tendency than the mean.
- 2 Marks Q39. Find the mode of a distribution where $l = 20, h = 10, f_1 = 15, f_0 = 6, f_2 = 6$.
- 2 Marks Q40. If each observation in a raw dataset is multiplied by $3$, how does it affect the mode of the dataset?
- 2 Marks Q41. Define an outlier. Between mean and median, which one is more affected by an extreme outlier?
- 2 Marks Q42. In a class test, the mean score of $40$ students is $50$. If the teacher adds $5$ bonus marks to each student's score, what is the new mean score?
- 2 Marks Q43. The weights of $10$ students are recorded. If one student weighing $45\text{ kg}$ leaves and a new student weighing $55\text{ kg}$ joins, how does the mean weight change?
- 2 Marks Q44. If an outlier is included in the dataset: $12, 15, 22, 44, 44, 48, 50, 51$, state which measure of central tendency changes significantly.
- 2 Marks Q45. Is it possible for the mean, median, and mode of a distribution to all be identical? Name such a distribution type
- 2 Marks Q46. If the sum of frequencies ($\sum f_i$) is $50$ and data is split into $5$ equal class intervals of width $10$, what is the lower boundary of the 4th class if the starting lower limit is $0$?
- 2 Marks Q47. Explain why class marks are used instead of individual observations when calculating the mean of grouped data.
- 2 Marks Q48. Can the cumulative frequency of a class ever decrease as we move down the table? Why?
- 2 Marks Q49. If the number of observations is odd, say $n = 25$, exactly which term represents the median?
- 2 Marks Q50. Write down the relationship between mean, median, and mode for a symmetrical distribution
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.