Data Handling

Data are collections of numbers or facts gathered to give information, such as the marks of a class, the favourite fruits of students or the number of books sold each day. In this chapter you learn to record data and organise it neatly. A list of raw observations is hard to read, so we use tally marks, drawing a vertical stroke for each item and crossing every group of four with a fifth stroke, and then count the frequency of each item in a frequency table. The chapter then shows two ways of presenting data visually. A pictograph uses pictures or symbols, where one symbol stands for a fixed number of objects given in a key, for example one picture of a cup = 10 cups of tea. A bar graph uses bars of uniform width with equal spacing, whose heights or lengths, read against a suitable scale such as 1 unit = 5 students, show the values. You will learn to interpret, draw and compare such graphs.

Detailed Worksheet: Data Handling Section A - Definitions (10 marks) 1. What is data? Give two examples of data you could collect in your school. (2 marks) 2. What are tally marks? Show how the number 13 is represented using tally marks. (2 marks) 3. What is a frequency table? Why is organising data into a table useful? (2 marks) 4. What is a pictograph? What is the use of a key in a pictograph? (2 marks) 5. What is a bar graph? Why must all bars in a bar graph have the same width? (2 marks) Section B - Calculations and Applications (15 marks) 6. The marks (out of 10) of 20 students in a test are: 5, 7, 8, 5, 6, 9, 10, 7, 8, 6, 7, 5, 9, 8, 7, 6, 7, 10, 8, 7. Prepare a frequency table using tally marks and answer: (i) how many students scored 7 marks (ii) which mark was obtained by the most students (iii) how many students scored 9 or more? (3 marks) 7. In a pictograph showing the number of cars sold by a showroom, one car symbol = 10 cars. Monday has 4 symbols, Tuesday has 6 symbols, Wednesday has 3.5 symbols and Thursday has 5 symbols. (i) Find the number of cars sold each day. (ii) Find the total number of cars sold. (iii) On which day were the fewest cars sold? (3 marks) 8. The number of students in Classes VI to X of a school are 135, 120, 95, 100 and 90. (i) Choose a suitable scale to draw a bar graph. (ii) What will be the height of the bar for Class VI using 1 unit = 10 students? (iii) Which class has the least number of students? (3 marks) 9. A bar graph shows the number of trees planted by an eco-club: 2019: 160, 2020: 200, 2021: 120, 2022: 250, 2023: 220. (i) In which year were the most trees planted? (ii) Find the difference between the trees planted in 2022 and 2021. (iii) Find the total number of trees planted in the five years. (3 marks) 10. In a survey of 30 students on their favourite colour, 9 chose blue, 7 chose red, 5 chose green, 6 chose yellow and the rest chose white. (i) How many chose white? (ii) If one symbol stands for 2 students, how many symbols will represent blue? (iii) Show the frequency of red in tally marks. (3 marks) Section C - Diagrams (10 marks) 11. Draw a bar graph for the following data on the number of books sold by a bookstore: Monday 40, Tuesday 55, Wednesday 30, Thursday 65, Friday 50. Use the scale 1 cm = 10 books. Label both axes and give the graph a title. (4 marks) 12. Draw a pictograph for the number of students absent from Class VI during a week: Monday 8, Tuesday 4, Wednesday 6, Thursday 2, Friday 10. Use one face symbol = 2 students and give a key. (3 marks) 13. Draw a horizontal bar graph showing the favourite fruits of a class: Banana 12, Mango 18, Apple 9, Orange 6. Use the scale 1 unit = 3 students. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A pictograph shows the number of wristwatches made by a factory using one clock symbol = 100 watches: Monday 6 symbols, Tuesday 4.5 symbols, Wednesday 5 symbols, Thursday 7 symbols. (i) Find the number of watches made each day. (ii) On which day was production highest and by how much was it more than on Tuesday? (iii) Why would a key of 1 symbol = 1 watch be unsuitable? (5 marks) 15. Two students drew bar graphs of the same data, the number of rainy days in five months (June 18, July 24, August 21, September 12, October 6). Student P used 1 unit = 2 days and Student Q used 1 unit = 6 days. (i) Find the bar heights for July in both graphs. (ii) Which scale makes the graph easier to draw on a small page? (iii) Which gives a more exact reading? Explain. (5 marks) 16. A class collected data on how students come to school: walk 15, bicycle 10, bus 20, car 5. (i) Organise the data in a table with tally marks. (ii) What fraction of the students come by bus? (iii) Suggest a reason for presenting this as a bar graph rather than as a list. (iv) If 10 more students start coming by bicycle next year, how will the bicycle bar change? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use graph paper for bar graphs, choose a suitable scale, and always give a key for pictographs.