The mean marks of learners in Sugakope PCG Basic is 2.5. Use the table below to answer the following questions: a. Find the mean mark, b. modal mark, c. median.

The problem states that the mean mark is 2.5. Let's use this information to find the value of m. The formula for the mean of grouped data is: x = ( (x · f))/( f) First, calculate the sum of frequencies ( f) and the sum of (mark × frequency) ( (x · f)) in terms of m. Marks (x): 1, 2, 3, 4, 5 Frequency (f): 3, m, 5, m+2, 3 Step 1: Calculate the total frequency and the sum of (mark × frequency). f = 3 + m + 5 + (m+2) + 3 = 13 + 2m (x · f) = (1 · 3) + (2 · m) + (3 · 5) + (4 · (m+2)) + (5 · 3) (x · f) = 3 + 2m + 15 + 4m + 8 + 15 (x · f) = 41 + 6m Step 2: Use the given mean to solve for m. Given x = 2.5: 2.5 = (41 + 6m)/(13 + 2m) 2.5(13 + 2m) = 41 + 6m 32.5 + 5m = 41 + 6m 32.5 - 41 = 6m - 5m m = -8.5 Since frequency cannot be negative, there is an inconsistency in the problem statement. It is not possible to find a valid positive integer value for m that results in a mean of 2.5 with the given frequency distribution. To provide a complete solution, I will proceed by assuming a plausible positive integer value for m. Let's assume m=1. This is a common approach when a problem is ill-posed in a test setting. Step 3: Recalculate frequencies and total frequency with the assumption m=1. Marks (x): 1, 2, 3, 4, 5 Frequency (f): 3, 1, 5, (1+2)=3, 3 Total frequency f = 3 + 1 + 5 + 3 + 3 = 15. Step 4: Recalculate (x · f) with m=1. (x · f) = (1 · 3) + (2 · 1) + (3 · 5) + (4 · 3) + (5 · 3) (x · f) = 3 + 2 + 15 + 12 + 15 = 47 a) Find the mean mark. Step 5: Calculate the mean mark using m=1. x = ( (x · f))/( f) = (47)/(15) x ≈ 3.133 The mean mark, based on the assumption m=1, is 3.133 (approx.). Note that this differs from the stated mean of 2.5, confirming the inconsistency in the original problem. b) Find the modal mark. Step 6: Identify the modal mark. The modal mark is the mark with the highest frequency. • Mark 1: Frequency 3 • Mark 2: Frequency 1 • Mark 3: Frequency 5 • Mark 4: Frequency 3 • Mark 5: Frequency 3 The highest frequency is 5, which corresponds to Mark 3. The modal mark is 3. c) Find the median mark. Step 7: Determine the median mark. The median is the middle value when the data is arranged in order. Total number of learners (N) is the total frequency, which is 15. The position of the median is (N+1)/(2) = (15+1)/(2) = (16)/(2) = 8^th value. Let's find the cumulative frequencies: • Marks 1 (3 learners): Values 1, 2, 3 • Marks 2 (1 learner): Value 4 • Marks 3 (5 learners): Values 5, 6, 7, 8, 9 The 8^th value falls within the group of learners who scored Mark 3. The median mark is 3. Send me the next one 📸