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
Step 1: Solve Question 3. To draw a histogram for the given data, follow these steps: • Draw a horizontal axis (x-axis) and label it "Score". Mark intervals corresponding to the class intervals: 50-60, 60-70, 70-80, 80-90, 90-100, 100-110. Since the classes are continuous and start from 50, you might need a kink (zig-zag) on the x-axis if starting from 0. • 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 50-60, draw a bar of height 2. • For 60-70, draw a bar of height 4. • For 70-80, draw a bar of height 9. • For 80-90, draw a bar of height 10. • For 90-100, draw a bar of height 7. • For 100-110, draw a bar of height 3. Step 2: Solve Question 4. First, we list the given heights: 160, 151, 150, 170, 179, 158, 172, 165, 162, 172, 160, 161, 152, 168, 170, 175, 167, 169, 158, 164, 176, 150, 164, 166, 165, 167, 165, 166, 162, 160, 168, 173, 162, 154, 151, 179, 172, 169, 165, 164. The lowest value is 150 cm and the highest value is 179 cm. We need to create class intervals of size 5, starting with a lower limit of 150. The intervals will be exclusive of the upper bound (e.g., 150-155 includes 150 but not 155). • 150-155: 150, 151, 150, 152, 154, 151 (Frequency: 6) • 155-160: 158, 158 (Frequency: 2) • 160-165: 160, 162, 160, 161, 164, 164, 162, 160, 162, 164 (Frequency: 10) • 165-170: 165, 168, 167, 169, 166, 165, 167, 165, 166, 168, 169, 165 (Frequency: 12) • 170-175: 170, 172, 172, 170, 175, 173, 172 (Frequency: 7) • 175-180: 179, 176, 179 (Frequency: 3) The grouped frequency distribution table 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 \\ Total & 40 \\ Step 3: Solve Question 5. To draw a histogram for the given data, follow these steps: • Draw a horizontal axis (x-axis) and label it "Height (in cm)". Mark intervals corresponding to the class intervals: 120-125, 125-130, 130-135, 135-140, 140-145, 145-150. • Draw a vertical axis (y-axis) and label it "Number of students". Choose a suitable scale (e.g., 1 unit = 1 student). • For each class interval, draw a rectangular bar whose width is equal to the class interval and whose height is proportional to the number of students (frequency). The bars should be adjacent to each other without any gaps. • For 120-125, draw a bar of height 2. • For 125-130, draw a bar of height 3. • For 130-135, draw a bar of height 8. • For 135-140, draw a bar of height 10. • For 140-145, draw a bar of height 13. • For 145-150, draw a bar of height 4. Step 4: Solve Question 6. From the given graph: • 1 hour: 4 students • 2 hours: 8 students • 3 hours: 22 students • 4 hours: 32 students • 5 hours: 8 students • 6 hours: 6 students • 7 hours: 4 students a) How many students watch TV for more than 4 hours? This includes students who watch for 5, 6, or 7 hours. Number of students = 8 + 6 + 4 = 18. The number of students who watch TV for more than 4 hours is 18. b) How many students watch TV for less than 4 hours? This includes students who watch for 1, 2, or 3 hours. Number of students = 4 + 8 + 22 = 34. The number of students who watch TV for less than 4 hours is 34. c) For how many hours the maximum number of students watch TV? The maximum number of students is 32, which corresponds to 4 hours of TV. The maximum number of students watch TV for 4 hours. d) For how many hours the minimum number of students watch TV? The minimum number of students is 4, which corresponds to 1 hour and 7 hours of TV. The minimum number of students watch TV for 1 hour and 7 hours. Send me the next one 📸