Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define the mean of a data set.
Correct! Mean is the sum of all observations divided by the number of observations.
(2) Find the median of the data: 12, 15, 18, 20, 22.
Perfect! The median is the middle value when data is arranged in order: 18.
(3) Find the mode of the data: 5, 7, 5, 9, 5, 10.
Excellent! 5 appears three times, making it the mode.
(4) State one difference between mean and median.
Calculation of Mean requires
Great! Mean is affected by all values including extremes, while median only depends on the middle value(s).
(5) A data set has values: 3, 7, 7, 10, 12. Write the range of the data.
Correct! Range = 12 - 3 = 9.
Short Answer Questions (2 Marks Each)
Answer each question with detailed calculations
(1) The marks obtained by 10 students in a test are: 12, 15, 18, 20, 22, 25, 18, 15, 20, 24. Find the mean.
Mean:
Excellent! Mean = (12+15+18+20+22+25+18+15+20+24) ÷ 10 = 189 ÷ 10 = 18.9.
(2) Find the median of the following data: 8, 12, 14, 16, 18, 20, 22, 24.
Median:
Perfect! For 8 values, median = (16 + 18) ÷ 2 = 17.
(3) Construct a frequency distribution table for the following marks obtained by 12 students: 12, 15, 15, 18, 18, 18, 20, 20, 22, 22, 24, 24.
| Marks | Frequency |
|---|---|
| 12 | |
| 15 | |
| 18 | |
| 20 | |
| 22 | |
| 24 |
(4) Find the mode for the data: 3, 4, 4, 5, 5, 5, 6, 7, 7.
Mode:
Correct! 5 appears three times, which is the highest frequency.
(5) The marks of 15 students in a mathematics test are: 10, 12, 14, 12, 15, 10, 12, 14, 15, 16, 12, 14, 15, 16, 18. Find the range of marks.
Range:
Great! Range = 18 - 10 = 8.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete steps and clear calculations.
(1) The marks obtained by 20 students are: 10, 12, 15, 15, 18, 18, 20, 22, 24, 24, 26, 28, 30, 30, 32, 32, 35, 36, 38, 40. Find the mean, median, and mode of the marks.
Mean:
Correct! Mean = 500 ÷ 20 = 25, Median = (24 + 26) ÷ 2 = 25, Mode = 15, 18, 24, 30, 32 (each appears twice).
(2) The following table shows marks obtained by students. Find the mean marks using class intervals.
| Marks | 0-10 | 11-20 | 21-30 | 31-40 | 41-50 |
|---|---|---|---|---|---|
| Students | 5 | 8 | 12 | 10 | 5 |
Mean marks:
Perfect! Using midpoints: Mean = (5×5 + 15.5×8 + 25.5×12 + 35.5×10 + 45.5×5) ÷ 40 = 1020 ÷ 40 = 25.5.
(3) The heights of 15 students (in cm) are: 140, 145, 142, 138, 150, 148, 146, 144, 142, 149, 147, 145, 143, 141, 140. Draw a frequency distribution table with given class intervals.
| Class Interval | Frequency |
|---|---|
| 138-140 | |
| 141-143 | |
| 144-146 | |
| 147-149 | |
| 150-152 |
(4) Find the mean marks in Maths and Science from the given student data.
Mean Maths:
Excellent! Maths mean = 168 ÷ 10 = 16.8, Science mean = 166 ÷ 10 = 16.6.
(5) Find the median daily sale from the frequency distribution.
| Daily Sale | 0-10 | 11-20 | 21-30 | 31-40 |
|---|---|---|---|---|
| Frequency | 2 | 5 | 7 | 4 |
Median:
Correct! Total = 18, median position = 9th and 10th values. Median class is 21-30. Using formula: Median ≈ 22.14.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The mean of the numbers 5, 7, 9, 11, 13 is:
(a) 9 (b) 10 (c) 11 (d) 12
Correct! Mean = (5+7+9+11+13) ÷ 5 = 45 ÷ 5 = 9.
(2) The median of the data 3, 5, 7, 9, 11, 13 is:
(a) 7 (b) 8 (c) 9 (d) 10
Correct! For 6 values, median = (7 + 9) ÷ 2 = 8.
(3) The mode of the data 4, 6, 6, 8, 10, 6, 12 is:
(a) 4 (b) 6 (c) 8 (d) 10
Correct! 6 appears three times, making it the mode.
(4) The range of 12, 15, 18, 20, 25 is:
(a) 10 (b) 12 (c) 13 (d) 15
Correct! Range = 25 - 12 = 13.
(5) A set of numbers has mean 20. If each number is increased by 5, the new mean is:
(a) 20 (b) 25 (c) 15 (d) 30
Correct! When each value increases by 5, the mean also increases by 5: 20 + 5 = 25.
(6) The marks of 6 students are: 12, 15, 18, 20, 22, 25. The median is:
(a) 18 (b) 19 (c) 20 (d) 21
Correct! Median = (18 + 20) ÷ 2 = 19.
(7) The sum of the observations in a data set is 150, and the number of observations is 10. The mean is:
(a) 10 (b) 15 (c) 20 (d) 25
Correct! Mean = Sum ÷ Number of observations = 150 ÷ 10 = 15.
(8) The mode of the data 2, 4, 4, 6, 8, 8, 8, 10 is:
(a) 4 (b) 6 (c) 8 (d) 10
Correct! 8 appears three times, which is the highest frequency.
(9) The class interval containing the median is called:
(a) Median class (b) Modal class (c) Frequency class (d) Range class
Correct! The class interval containing the median is called the median class.
(10) If the data is 5, 7, 9, 11, 13, 15, the mean is:
(a) 9 (b) 10 (c) 11 (d) 12
Correct! Mean = (5+7+9+11+13+15) ÷ 6 = 60 ÷ 6 = 10.
Advanced Statistics Challenge
Determine whether these statements are True or False: