A class of 45 students sat a test. The marks and their frequencies are shown in the table. Find the value of x and calculate the mean mark.

Right maame, let's go. Step 1: Find the value of x. The total number of students is given as 45. This means the sum of all frequencies must be equal to 45. 6 + (x^2-1) + 3x + 10 + (3x-2) + 5 = 45 Combine the constant terms and the terms with x: x^2 + (3x+3x) + (6-1+10-2+5) = 45 x^2 + 6x + 18 = 45 Subtract 45 from both sides to form a quadratic equation: x^2 + 6x - 27 = 0 Factor the quadratic equation: (x+9)(x-3) = 0 This gives two possible values for x: x = -9 or x = 3 Frequencies cannot be negative. Let's check the frequencies for each value of x: If x = -9: Frequency for mark 17 is 3x = 3(-9) = -27, which is not possible. If x = 3: Frequency for mark 16 is x^2-1 = (3)^2-1 = 9-1 = 8. Frequency for mark 17 is 3x = 3(3) = 9. Frequency for mark 19 is 3x-2 = 3(3)-2 = 9-2 = 7. All these frequencies are positive, so x=3 is the correct value. Step 2: Calculate the mean. First, update the frequencies using x=3: • Mark 15: Frequency = 6 • Mark 16: Frequency = 3^2-1 = 8 • Mark 17: Frequency = 3(3) = 9 • Mark 18: Frequency = 10 • Mark 19: Frequency = 3(3)-2 = 7 • Mark 20: Frequency = 5 The mean (m) is calculated using the formula m = ( (m · f))/( f), where m is the mark and f is the frequency. Calculate the sum of (mark × frequency): (m · f) = (15 × 6) + (16 × 8) + (17 × 9) + (18 × 10) + (19 × 7) + (20 × 5) (m · f) = 90 + 128 + 153 + 180 + 133 + 100 (m · f) = 784 The total frequency is f = 6+8+9+10+7+5 = 45. Now, calculate the mean: m = (784)/(45) m ≈ 17.4222... Rounding the mean to 1 decimal place: m ≈ 17.4 The value of x is 3 The mean, corrected to 1 decimal place, is 17.4 Send me the next one 📸