This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Step 1: Solve Question 1. From the given histogram for daily earnings of 100 workers: • 100-150 Rs: 30 workers • 150-200 Rs: 40 workers • 200-250 Rs: 15 workers • 250-300 Rs: 10 workers • 300-350 Rs: 5 workers a) In which earning group are maximum workers? The highest bar corresponds to the 150-200 Rs group with 40 workers. The maximum number of workers are in the earning group 150-200 Rs. b) What is the size of the classes? The class size is the difference between the upper and lower limits of any class interval. For example, for the 100-150 Rs class, the size is 150 - 100 = 50. The size of the classes is 50 Rs. c) How many workers are in the maximum earning group? The maximum earning group is 300-350 Rs. There are 5 workers in the maximum earning group. d) How many workers earn less than ₹ 200? This includes workers in the 100-150 Rs and 150-200 Rs groups. Number of workers = 30 + 40 = 70. 70 workers earn less than ₹ 200. e) How many workers earn ₹ 200 or more? This includes workers in the 200-250 Rs, 250-300 Rs, and 300-350 Rs groups. Number of workers = 15 + 10 + 5 = 30. 30 workers earn ₹ 200 or more. Step 2: Solve Question 2. From the given histogram for runs scored by a cricket player: • 0-20 runs: 1 match • 20-40 runs: 6 matches • 40-60 runs: 9 matches • 60-80 runs: 4 matches • 80-100 runs: 2 matches a) How many matches did he play in the highest runs group? The highest runs group is 80-100 runs. He played 2 matches in the highest runs group. b) How many matches did he play? Total number of matches = 1 + 6 + 9 + 4 + 2 = 22. He played a total of 22 matches. c) In how many matches did he score 60 or more runs? This includes matches in the 60-80 runs and 80-100 runs groups. Number of matches = 4 + 2 = 6. He scored 60 or more runs in 6 matches. d) In how many matches did he score less than 40 runs? This includes matches in the 0-20 runs and 20-40 runs groups. Number of matches = 1 + 6 = 7. He scored less than 40 runs in 7 matches. Step 3: Solve Question 7. To construct a histogram from the grouped frequency distribution table prepared in Q.4: The table from Q.4 is: |c|c| Height (in cm) & Frequency \\ 150-155 & 6 \\ 155-160 & 2 \\ 160-165 & 10 \\ 165-170 & 12 \\ 170-175 & 7 \\ 175-180 & 3 \\ Follow these steps to draw the histogram: • Draw a horizontal axis (x-axis) and label it "Height (in cm)". Mark intervals corresponding to the class intervals: 150-155, 155-160, 160-165, 165-170, 170-175, 175-180. • Draw a vertical axis (y-axis) and label it "Frequency". Choose a suitable scale (e.g., 1 unit = 1 frequency). • For each class interval, draw a rectangular bar whose width is equal to the class interval and whose height is proportional to its frequency. The bars should be adjacent to each other without any gaps. • For 150-155, draw a bar of height 6. • For 155-160, draw a bar of height 2. • For 160-165, draw a bar of height 10. • For 165-170, draw a bar of height 12. • For 170-175, draw a bar of height 7. • For 175-180, draw a bar of height 3. Drop the next question.