Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define frequency in the context of data handling. Frequency is the
(2) What is the range of the data: 45, 38, 52, 40?
Correct! Range = 52 - 38 = 14.
(3) Which type of graph uses pictures or symbols to represent data?
Perfect! Pictographs use pictures or symbols to represent data.
(4) Which type of data is collected directly from the source?
Excellent! Primary data is collected firsthand from the original source.
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) Write the tally marks for: 13, 17, 24, 29.
(2) The number of books borrowed from a library in four months is: Jan – 45, Feb – 38, Mar – 50, Apr – 42. Represent this data using tally marks.
(3) A coin is tossed 20 times and the results are: Head – 11, Tail – 9. Represent the data using a bar graph.
(4) A class survey showed that 8 students walk to school, 12 cycle, and 5 come by bus. Represent this data using a pictograph.
(5) The following are the marks scored by 8 students: 12, 15, 18, 10, 14, 16, 13, 19. Find the range and total frequency. Range =
Perfect! Range = 9, Total frequency = 8.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) The marks scored by 20 students are: 15, 12, 18, 10, 14, 15, 16, 13, 19, 17, 12, 18, 16, 15, 14, 13, 17, 19, 12, 18. Prepare a frequency table using tally marks and find the highest frequency.
Highest frequency:
Perfect! The highest frequency is 3.
(2) The daily production (in kg) of a factory for 6 days is: 250, 300, 280, 320, 290, 310. Represent this data using a bar graph and find the range.
Range:
(3) The favourite fruits of 25 students are: Mango – 10, Apple – 6, Orange – 5, Banana – 4. Represent the data using a pictograph (choose a suitable symbol).
(4) The number of wickets taken by a bowler in 8 matches are: 2, 3, 5, 4, 3, 2, 6, 5. Make a frequency table, draw a bar graph, and find the total wickets taken.
Total wickets:
(5) The heights (in cm) of 12 saplings are: 25, 30, 28, 32, 26, 29, 35, 33, 31, 27, 34, 30. Prepare a tally table, find the range, and represent the data using a bar graph. Range:
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The range of 45, 38, 52, 40 is:
(a) 14 (b) 12 (c) 10 (d) 15
Correct! Range = 52 - 38 = 14.
(2) The mean of 7 numbers is 12. If one number 18 is removed from the data set, what is the new mean?
(a) 10.5 (b) 11 (c) 11.5 (d) 12
Correct! Sum of 7 numbers = 7 × 12 = 84. After removing 18: Sum = 84 - 18 = 66. New mean = 66 ÷ 6 = 11.
(3) The highest bar in a bar graph shows:
(a) Lowest value (b) Highest value (c) Range (d) Average
Correct! The highest bar represents the highest frequency or value.
(4) Which is a secondary data source?
(a) Survey in your school (b) Data from a newspaper (c) Data from your notebook (d) Marks you record from a test you conducted
Correct! Newspaper data is secondary - collected and published by others.
(5) In a pictograph, if 1 picture = 10 students, then 7 pictures represent:
(a) 70 students (b) 17 students (c) 77 students (d) 700 students
Correct! 7 pictures × 10 students per picture = 70 students.
(6) Which of these is NOT used to represent data?
(a) Tally marks (b) Pictograph (c) Bar graph (d) Division sum
Correct! Division sum is a mathematical operation, not a data representation method.
(7) The sum of all frequencies in a data set is called:
(a) Total frequency (b) Range (c) Mode (d) Mean
Correct! Total frequency is the sum of all individual frequencies.
(8) Which type of data is collected from already published sources?
(a) Primary data (b) Secondary data (c) Tertiary data (d) Observed data
Correct! Secondary data comes from already published or existing sources.
(9) If the range of a data set is 25 and the smallest value is 8, what is the largest value?
(a) 17 (b) 25 (c) 33 (d) 42
Correct! Range = Largest value - Smallest value. So 25 = Largest value - 8. Therefore, Largest value = 25 + 8 = 33.
(10) If the range of a data set is 15 and the lowest value is 25, then the highest value is:
(a) 35 (b) 40 (c) 45 (d) 50
Correct! Highest value = Lowest value + Range = 25 + 15 = 40.
Complex Data Analysis True or False
Determine whether these statements are True or False:
Data Handling - Hard Quiz
🎉 Outstanding Mastery! Advanced Data Handling Excellence Achieved:
You have successfully conquered the "Data Handling (Hard)" worksheet and mastered:
(1) Advanced Frequency Analysis: Understanding and calculating frequencies for complex datasets with repeated values
(2) Sophisticated Tally Systems: Working efficiently with large numbers using advanced tally mark grouping techniques
(3) Complex Frequency Table Construction: Creating detailed frequency tables with multiple categories and accurate tallying
(4) Advanced Range Applications: Calculating range for diverse datasets and using range in reverse calculations
(5) Multi-dimensional Data Representation: Constructing complex bar graphs, pictographs, and tally charts for varied data types
(6) Scaled Data Visualization: Creating and interpreting pictographs with sophisticated scaling systems
(7) Comprehensive Data Analysis: Performing complete analysis including frequency tables, graphs, and statistical measures
(8) Advanced Problem-solving: Solving multi-step problems involving data collection, organization, and representation
(9) Statistical Relationship Understanding: Connecting frequency, range, and total frequency in meaningful ways
(10) Complex Real-world Applications: Working with practical datasets from sports, business, academics, and science
(11) Advanced Graph Interpretation: Reading and analyzing complex patterns in bar graphs and pictographs
(12) Data Source Evaluation: Clearly distinguishing between primary and secondary data sources in various contexts
(13) Mathematical Precision: Maintaining accuracy in complex calculations involving large datasets
(14) Advanced Pictograph Scaling: Understanding and applying sophisticated symbol-to-value relationships
(15) Comprehensive Data Organization: Systematically organizing complex datasets using multiple representation methods
(16) Statistical Reasoning: Making logical connections between different aspects of data analysis
(17) Multi-step Data Processing: Handling problems requiring multiple analytical techniques
(18) Advanced Mathematical Communication: Using precise statistical vocabulary and expressing complex data relationships
(19) Analytical Thinking: Developing sophisticated approaches to data interpretation and analysis
Exceptional achievement! You've mastered advanced data handling with sophisticated analytical reasoning!