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.
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Okay faith, let's break down Question 1(a) from your assignment. Question 1(a): In 503 exam, the scores obtained were later grouped into classes as follows: | Class Interval | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 | |---|---|---|---|---|---|---|---|---|---| | Frequency (f) | 3 | 4 | 5 | 8 | 12 | 9 | 6 | 2 | 1 | Using an assumed mean of 38, calculate the: (i) Mean (ii) Median (iii) Standard deviation (iv) Interpret the students performance (v) When is median preferred to mean as a performance indicator? First, let's set up a table to calculate midpoints (x), deviations (d = x - A), fd, d^2, and fd^2. Assumed Mean (A) = 38 Class width (i) = 5 | Class Interval | f | x (midpoint) | d = x - 38 | fd | d^2 | fd^2 | cf | |:---------------|:-:|:------------:|:----------:|:----:|:-----:|:------:|:--:| | 16-20 | 3 | 18 | -20 | -60 | 400 | 1200 | 3 | | 21-25 | 4 | 23 | -15 | -60 | 225 | 900 | 7 | | 26-30 | 5 | 28 | -10 | -50 | 100 | 500 | 12 | | 31-35 | 8 | 33 | -5 | -40 | 25 | 200 | 20 | | 36-40 | 12| 38 | 0 | 0 | 0 | 0 | 32 | | 41-45 | 9 | 43 | 5 | 45 | 25 | 225 | 41 | | 46-50 | 6 | 48 | 10 | 60 | 100 | 600 | 47 | | 51-55 | 2 | 53 | 15 | 30 | 225 | 450 | 49 | | 56-60 | 1 | 58 | 20 | 20 | 400 | 400 | 50 | | Total | N=50 | | | -15| | 4475 | | (i) Mean Step 1: Use the formula for mean with an assumed mean. X = A + ( fd)/(N) Step 2: Substitute the values from the table. X = 38 + (-15)/(50) Step 3: Calculate the mean. X = 38 - 0.3 = 37.7 The mean score is 37.7. (ii) Median Step 1: Determine the median position and median class. The total frequency N = 50, so the median position is (N)/(2) = (50)/(2) = 25. From the cumulative frequency (cf) column, the 25th score falls into the 36-40 class interval (cf = 32). Median class = 36-40. Step 2: Identify the values for the median formula. Lower class boundary of