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
Okay, Janet, let's re-examine this problem with a closer look at the text. It appears the initial statement reads: "The mean are 25 learners in Sugakope PCG Basic 19-52. Use the table below to answer the following questions." This means the total number of learners is 25, which is the sum of all frequencies. This is a crucial piece of information that allows us to find the value of m. Marks (x): 1, 2, 3, 4, 5 Frequency (f): 3, m, 5, m+2, 3 Step 1: Calculate the total frequency in terms of m and set it equal to 25. f = 3 + m + 5 + (m+2) + 3 f = 13 + 2m Given that the total number of learners is 25: 13 + 2m = 25 2m = 25 - 13 2m = 12 m = (12)/(2) m = 6 Step 2: Substitute m=6 into the frequency distribution to get the actual frequencies. • Mark 1: Frequency = 3 • Mark 2: Frequency = m = 6 • Mark 3: Frequency = 5 • Mark 4: Frequency = m+2 = 6+2 = 8 • Mark 5: Frequency = 3 Let's verify the total frequency: 3 + 6 + 5 + 8 + 3 = 25. This matches the given total number of learners. a) Find the mean mark. Step 3: Calculate the sum of (mark × frequency). (x · f) = (1 · 3) + (2 · 6) + (3 · 5) + (4 · 8) + (5 · 3) (x · f) = 3 + 12 + 15 + 32 + 15 (x · f) = 77 Step 4: Calculate the mean mark. x = ( (x · f))/( f) = (77)/(25) x = 3.08 The mean mark is 3.08. b) Find the modal mark. Step 5: Identify the modal mark. The modal mark is the mark with the highest frequency. • Mark 1: Frequency 3 • Mark 2: Frequency 6 • Mark 3: Frequency 5 • Mark 4: Frequency 8 • Mark 5: Frequency 3 The highest frequency is 8, which corresponds to Mark 4. The modal mark is 4. c) Find the median mark. Step 6: Determine the median mark. The median is the middle value when the data is arranged in order. Total number of learners (N) is 25. The position of the median is (N+1)/(2) = (25+1)/(2) = (26)/(2) = 13^th value. Let's find the cumulative frequencies to locate the 13^th value: • Marks 1 (3 learners): Values 1st to 3rd • Marks 2 (6 learners): Values 4th to (3+6)=9th • Marks 3 (5 learners): Values 10th to (9+5)=14th The 13^th value falls within the group of learners who scored Mark 3. The median mark is 3. That's 2 down. 3 left today — send the next one.