Calculate the mean mark of the distribution (correct to one decimal place). Find the median mark. State the modal mark.

Here are the solutions to Question 4 and Question 5. Question 4 a) Calculate the mean mark of the distribution (correct to one decimal place). Step 1: Calculate the sum of (mark × frequency) for all marks. fx = (10 × 5) + (20 × 8) + (30 × 12) + (40 × 15) + (50 × 6) + (60 × 4) fx = 50 + 160 + 360 + 600 + 300 + 240 fx = 1710 Step 2: Calculate the total frequency. f = 5 + 8 + 12 + 15 + 6 + 4 = 50 Step 3: Calculate the mean mark. Mean = ( fx)/( f) = (1710)/(50) = 34.2 The mean mark is 34.2. b) Find the median mark. Step 1: Determine the position of the median. The total number of students is N=50. Since N is even, the median is the average of the (N)/(2)-th and ((N)/(2)+1)-th values. (N)/(2) = (50)/(2) = 25 (N)/(2) + 1 = 25 + 1 = 26 The median is the average of the 25th and 26th marks. Step 2: Find the marks corresponding to the 25th and 26th positions using cumulative frequency. • Marks 1-5 are 10. • Marks 6-13 are 20. • Marks 14-25 are 30. • Marks 26-40 are 40. The 25th mark is 30. The 26th mark is 40. Step 3: Calculate the median. Median = 25th mark + 26th mark2 = (30 + 40)/(2) = (70)/(2) = 35 The median mark is 35. c) State the modal mark. Step 1: Identify the mark with the highest frequency. From the table, the highest frequency is 15, which corresponds to the mark of 40. The modal mark is 40. Question 5 a) Form a pair of simultaneous equations to represent the information. Let A be the cost of one pen of type A and B be the cost of one pen of type B. From the first statement: "Four pens of type A and three pens of type B cost N2,100." 4A + 3B = 2100 (1) From the second statement: "Two pens of type A and five pens of type B cost N1,750." 2A + 5B = 1750 (2) The pair of simultaneous equations is: 4A + 3B &= 2100 \\ 2A + 5B &= 1750 b) Solve the equations to find the cost of one pen of type A and one pen of type B. Step 1: Multiply equation (2) by 2 to eliminate A. 2 × (2A + 5B) = 2 × 1750 4A + 10B = 3500 (3) Step 2: Subtract equation (1) from equation (3). (4A + 10B) - (4A + 3B) = 3500 - 2100 7B = 1400 Step 3: Solve for B. B = (1400)/(7) = 200 The cost of one pen of type B is N200. Step 4: Substitute the value of B into equation (2) to solve for A. 2A + 5(200) = 1750 2A + 1000 = 1750 2A = 1750 - 1000 2A = 750 Step 5: Solve for A. A = (750)/(2) = 375 The cost of one pen of type A is N375. The cost of one pen of type A is N375 and one pen of type B is N200. c) If a customer buys 6 pens of type A and 2 pens of type B, how much will he pay? Step 1: Use the costs found in part (b). Cost of 6 pens of type A = 6 × A = 6 × 375 Cost of 2 pens of type B = 2 × B = 2 × 200 Step 2: Calculate the total cost. Total cost = (6 × 375) + (2 × 200) Total cost = 2250 + 400 Total cost = 2650 The customer will pay N2,650. Send me the next one 📸