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
Welcome back JNR — been a while! Let's pick up where you left off. Here is the solution to question 10: First, let's list all the given data points and sort them in ascending order: Data: 0, 0, 1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 10 Total number of students ( f) = 29. a) To construct a frequency distribution table, we count how many times each score appears. Step 1: Construct the frequency distribution table. |c|c| Score (x) & Frequency (f) \\ 0 & 2 \\ 1 & 1 \\ 2 & 3 \\ 3 & 1 \\ 4 & 1 \\ 5 & 5 \\ 6 & 6 \\ 7 & 4 \\ 8 & 2 \\ 9 & 3 \\ 10 & 1 \\ Total & 29 \\ b) i) To state the modal score, we find the score with the highest frequency. Step 2: Identify the modal score. From the frequency table, the highest frequency is 6, which corresponds to the score of 6. The modal score is 6. ii) To calculate the probability that a student scored more than 5 marks, we count the number of students who scored 6, 7, 8, 9, or 10, and divide by the total number of students. Step 3: Calculate the probability of scoring more than 5 marks. Number of students who scored more than 5 marks = (Frequency of 6) + (Frequency of 7) + (Frequency of 8) + (Frequency of 9) + (Frequency of 10) Number of students who scored more than 5 marks = 6 + 4 + 2 + 3 + 1 = 16 Total number of students = 29 Probability = Number of students scoring > 5Total number of students = (16)/(29) The probability is 1629. c) To calculate the arithmetic mean using an assumed mean of 6, we use the formula x = A + ( fd)/( f), where A is the assumed mean, f is the frequency, and d = x - A is the deviation. Step 4: Calculate the deviations (d) and fd values. Assumed mean (A) = 6. |c|c|c|c| Score (x) & Frequency (f) & d = x - 6 & fd \\ 0 & 2 & -6 & -12 \\ 1 & 1 & -5 & -5 \\ 2 & 3 & -4 & -12 \\ 3 & 1 & -3 & -3 \\ 4 & 1 & -2 & -2 \\ 5 & 5 & -1 & -5 \\ 6 & 6 & 0 & 0 \\ 7 & 4 & 1 & 4 \\ 8 & 2 & 2 & 4 \\ 9 & 3 & 3 & 9 \\ 10 & 1 & 4 & 4 \\ Total & 29 & & -18 \\ Step 5: Calculate the arithmetic mean. fd = -18 f = 29 x = A + ( fd)/( f) x = 6 + (-18)/(29) x = 6 - (18)/(29) x = 6 - 0.620689... x ≈ 5.379 The arithmetic mean score is approximately 5.38. Drop the next question! 📸