Data Handling

Data handling is about collecting, organising and presenting information so that it can be understood quickly. In this chapter you will arrange raw data into a grouped frequency distribution using class intervals such as 10-20 and 20-30, where the upper limit belongs to the next class, and learn the meaning of class size, lower limit and upper limit. You will draw histograms, bar graphs without gaps for grouped data, and read information from them. You will also draw and interpret pie charts, in which each sector has a central angle equal to (value/total) x 360 degrees. The last part of the chapter introduces chance and probability. You will study random experiments such as tossing a coin, throwing a die or spinning a wheel, list their equally likely outcomes, and find the probability of an event as the number of favourable outcomes divided by the total number of outcomes. You will also see how probability helps in weather forecasts, quality checks and lucky draws.

Detailed Worksheet: Data Handling Section A - Definitions (10 marks) 1. Define data, raw data and frequency of an observation. (2 marks) 2. Define class interval and class size. For the class interval 20-30, write the lower limit, the upper limit and the class size. (2 marks) 3. What is a histogram? Give two differences between a histogram and a bar graph. (2 marks) 4. What is a pie chart? Write the formula for the central angle of a sector of a pie chart. (2 marks) 5. Define a random experiment, an outcome and an event. Write the formula for the probability of an event when outcomes are equally likely. (2 marks) Section B - Calculations and Applications (15 marks) 6. The weights (in kg) of 20 students are: 38, 41, 45, 52, 47, 39, 44, 50, 56, 43, 48, 42, 55, 40, 46, 51, 49, 37, 53, 45. Make a grouped frequency distribution with classes 35-40, 40-45, 45-50, 50-55 and 55-60. Which class has the highest frequency, and how many students weigh 50 kg or more? (3 marks) 7. A family's monthly income of Rs 20,000 is spent as follows: food Rs 8,000, rent Rs 5,000, education Rs 3,000, savings Rs 2,000 and others Rs 2,000. Find the central angle of each sector for a pie chart. (3 marks) 8. A pie chart shows the favourite sports of 360 students. The central angles are cricket 120 degrees, football 90 degrees, hockey 60 degrees and others 90 degrees. Find the number of students in each group. (3 marks) 9. A bag contains 4 red, 3 blue and 5 green balls of the same size. One ball is drawn at random. Find the probability that it is (i) red (ii) blue (iii) not green. (3 marks) 10. A die is thrown once. Find the probability of getting (i) a prime number (ii) a number greater than 4 (iii) a number other than 6. (3 marks) Section C - Diagrams (10 marks) 11. Draw a histogram for the grouped frequency distribution you made in Question 6. Label both axes and choose a suitable scale. (4 marks) 12. In a class of 36 students, 15 like chocolate ice cream, 9 like vanilla, 6 like strawberry and 6 like mango. Find the central angles and draw a pie chart. (3 marks) 13. Draw a circular spinner divided into 8 equal sectors numbered 1 to 8. Find the probability that the pointer stops on (i) an even number (ii) a number greater than 6 (iii) a prime number. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. The heights (in cm) of 50 students are grouped as follows: 135-140: 4 students, 140-145: 10, 145-150: 18, 150-155: 12, 155-160: 6. (i) What is the class size? (ii) Which class has the maximum number of students? (iii) How many students are shorter than 145 cm? (iv) What percentage of students are 150 cm or taller? (v) Why is a histogram, and not an ordinary bar graph, used for this data? (5 marks) 15. For each data set, decide whether a pie chart, a bar graph or a histogram is most suitable, and justify your choice: (i) monthly rainfall in a city for the 12 months of a year (ii) how a student spends the 24 hours of a day (iii) the ages of the people in a colony grouped as 0-10, 10-20, 20-30 and so on. Explain why a pie chart is suitable only when the parts make up a whole. (5 marks) 16. Sohan tossed a coin 50 times and got 27 heads. Find the fraction of tosses that gave heads and compare it with the theoretical probability of getting a head. Explain why the two values are not exactly equal and what would happen if he tossed the coin 1000 times. In a lucky draw with 1000 tickets, Sohan holds 5 tickets; find the probability that he wins. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Draw graphs on graph paper with a ruler and protractor, and write probabilities as fractions in their lowest terms.