Data Handling

Data handling is about collecting, organising, representing and interpreting information. You will organise raw data in frequency tables and find a representative value, a single value that represents the whole data. The arithmetic mean, or average, is the sum of all observations divided by the number of observations, so the mean of 4, 6, 8 and 10 is 7. The range is the difference between the highest and lowest observations. The mode is the observation that occurs most often, and the median is the middle value when the data are arranged in ascending or descending order. You will also draw and read bar graphs with a suitable scale, and double bar graphs that compare two sets of data side by side, such as marks in two terms. Finally, the chapter introduces chance and probability: when a coin is tossed, getting a head or a tail is equally likely, so the probability of a head is 1/2, and when a die is thrown, each number from 1 to 6 has a probability of 1/6.

Detailed Worksheet: Data Handling Section A - Definitions (10 marks) 1. What is the arithmetic mean? Write its formula. (2 marks) 2. Define range and mode of a set of data. (2 marks) 3. What is the median? How is it found for an odd number of observations? (2 marks) 4. What is a double bar graph? When is it useful? (2 marks) 5. What is probability? What are equally likely outcomes? (2 marks) Section B - Calculations and Applications (15 marks) 6. The heights (in cm) of 7 students are 152, 140, 148, 155, 150, 145 and 160. Find (i) the mean height (ii) the range (iii) the median. (3 marks) 7. The marks of 15 students out of 10 are: 2, 3, 6, 7, 3, 5, 7, 3, 9, 8, 7, 3, 7, 6, 3. Find (i) the mode (ii) the median (iii) the mean, correct to one decimal place. (3 marks) 8. A batsman scored the following runs in 6 innings: 58, 76, 40, 35, 46, 45. Find (i) his mean score (ii) the range of his scores (iii) how many runs he must score in the 7th innings to raise his mean to 52. (3 marks) 9. A die is thrown once. Find the probability of getting (i) the number 5 (ii) an even number (iii) a number greater than 4. A coin is tossed once; find the probability of getting a tail. (3 marks) 10. The mean of five numbers is 27. If one number is excluded, the mean becomes 25. Find the excluded number. Also find the mean of the first ten natural numbers. (3 marks) Section C - Diagrams (10 marks) 11. Draw a double bar graph to compare the marks of a student in two terms: English (72, 80), Hindi (65, 70), Maths (85, 92), Science (78, 75), Social Science (70, 78). Use a suitable scale. In which subject did the marks fall? (4 marks) 12. Draw a bar graph showing the number of students who chose each favourite sport: cricket 18, football 12, badminton 8, hockey 6, kabaddi 4. State the mode. (3 marks) 13. Draw a frequency table using tally marks for the shoe sizes of 20 students: 5, 6, 6, 7, 5, 8, 6, 7, 6, 5, 7, 8, 6, 6, 7, 5, 6, 9, 7, 6. Find the mode. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. The daily wages (in Rs) of 7 workers are 500, 520, 480, 510, 490, 500 and 2600 (the supervisor). (i) Find the mean. (ii) Find the median. (iii) Which value better represents a typical worker's wage? Why? (iv) What effect does one very large value have on the mean? (5 marks) 15. A shopkeeper sells shoes of sizes 5 to 10. (i) Which representative value, mean, median or mode, will help him decide which size to stock most? (ii) Why is the mean not useful here? (iii) Give one situation where the mean is the best choice. (iv) Give one where the median is the best choice. (5 marks) 16. A bag contains 4 red, 3 blue and 5 green balls of the same size. (i) Find the total number of balls. (ii) Find the probability of drawing a green ball. (iii) Which colour is least likely to be drawn? (iv) If 2 more blue balls are added, what is the new probability of drawing a blue ball? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Arrange data in order before finding the median, and use graph paper for bar graphs.