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.
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Here are the solutions to the problems. 3. The table shows marks got by a group of pupils from a test. | Mark | Number of pupils | | :--- | :--------------- | | 20 | 2 | | 30 | 4 | | 40 | 2 | a) How many pupils were in that group? Step 1: Sum the number of pupils. Total pupils = 2 + 4 + 2 = 8 There were 8 pupils in that group. b) Calculate the average mark score. Step 1: Calculate the total marks obtained by all pupils. Total marks = (20 × 2) + (30 × 4) + (40 × 2) Total marks = 40 + 120 + 80 Total marks = 240 Step 2: Calculate the average mark score. Average mark = Total marksTotal pupils = (240)/(8) Average mark = 30 The average mark score is 30. c) Find the median mark. Step 1: List all the marks in ascending order. The marks are: 20, 20, 30, 30, 30, 30, 40, 40. There are 8 marks in total. Step 2: Identify the middle values. Since there is an even number of marks (8), the median is the average of the two middle values (the 4th and 5th values). The 4th value is 30. The 5th value is 30. Step 3: Calculate the median. Median = (30 + 30)/(2) = (60)/(2) = 30 The median mark is 30. 4. Subtract 140kg, 8Hg and 9726mg from 160kg 8Hg and 8692mg. Step 1: Write the quantities for subtraction. We need to calculate: (160 kg 8 Hg 8692 mg) - (140 kg 8 Hg 9726 mg). Step 2: Perform subtraction for milligrams (mg). Since 8692 mg < 9726 mg, we need to borrow from the hectograms (Hg). 1 Hg = 100 g = 100,000 mg. Borrow 1 Hg from 8 Hg, leaving 7 Hg. Add 100,000 mg to 8692 mg. 8692 mg + 100,000 mg = 108692 mg. Now, 108692 mg - 9726 mg = 98966 mg. Step 3: Perform subtraction for hectograms (Hg). We now have 7 Hg in the first quantity. Since 7 Hg < 8 Hg, we need to borrow from kilograms (kg). 1 kg = 10 Hg. Borrow 1 kg from 160 kg, leaving 159 kg. Add 10 Hg to 7 Hg. 7 Hg + 10 Hg = 17 Hg. Now, 17 Hg - 8 Hg = 9 Hg. Step 4: Perform subtraction for kilograms (kg). We now have 159 kg in the first quantity. 159 kg - 140 kg = 19 kg. The final result is 19 kg 9 Hg 98966 mg. 5. Use the above line graph (Collected eggs for five days) to answer the questions. Read the