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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The problem states "30 J.H.S. 2 pupils" but only 19 scores are provided in the data. We will proceed with the 19 given scores. The given scores are: 5, 3, 2, 4, 5, 2, 3, 3, 4, 2, 1, 3, 3, 4, 2, 3, 4, 3, 1 A) Construct a frequency table for the data. Step 1: Count the frequency of each score. • Score 1: Appears 2 times • Score 2: Appears 4 times • Score 3: Appears 7 times • Score 4: Appears 4 times • Score 5: Appears 2 times The total number of scores is 2+4+7+4+2 = 19. Step 2: Create the frequency table. |c|c| Score (x) & Frequency (f) \\ 1 & 2 \\ 2 & 4 \\ 3 & 7 \\ 4 & 4 \\ 5 & 2 \\ Total & 19 \\ The frequency table is shown above. B) Find the median marks. Step 1: Determine the position of the median. Since the total number of scores (N) is 19 (an odd number), the median is the value at the (N+1)/(2) position. Median position = (19+1)/(2) = (20)/(2) = 10^th The median is the 10th score when the data is arranged in ascending order. Step 2: Find the 10th score. Let's list the scores in ascending order using the frequency table: 1, 1 (2 scores) 2, 2, 2, 2 (next 4 scores, cumulative total: 2+4=6 scores) 3, 3, 3, 3, 3, 3, 3 (next 7 scores, cumulative total: 6+7=13 scores) The 10th score falls within the group of scores that are 3. Specifically, the 7th score is 3, the 8th is 3, the 9th is 3, and the 10th score is 3. The median mark is 3. C) Calculate the mean of the distribution. Step 1: Calculate the sum of (score × frequency) for all scores. We add an fx column to the frequency table: |c|c|c| Score (x) & Frequency (f) & fx \\ 1 & 2 & 1 × 2 = 2 \\ 2 & 4 & 2 × 4 = 8 \\ 3 & 7 & 3 × 7 = 21 \\ 4 & 4 & 4 × 4 = 16 \\ 5 & 2 & 5 × 2 = 10 \\ Total & f = 19 & fx = 2+8+21+16+10 = 57 \\ Step 2: Calculate the mean using the formula x = ( fx)/( f). x = (57)/(19) x = 3 The mean of the distribution is 3. Send me the next one 📸