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 😘Amanda — been a while! Let's pick up where you left off. First, let's sort the marks for both Thandiwe and Anna to make calculations easier. Thandiwe's marks (sorted): 3, 5, 10, 10, 11, 12, 14, 16, 19, 20 Anna's marks (sorted): 11, 11, 11, 12, 12, 12, 12, 13, 13, 13 a) Calculate the mean, median, range, IQR, and mode for both sets of marks. Step 1: Calculate for Thandiwe's marks. There are n=10 marks. • Mean: Sum of marks divided by the number of marks. Mean = (3+5+10+10+11+12+14+16+19+20)/(10) = (120)/(10) = 12 • Median: The middle value of the sorted data. Since there are 10 marks (an even number), the median is the average of the 5th and 6th values. Median = (11+12)/(2) = (23)/(2) = 11.5 • Range: The difference between the highest and lowest marks. Range = 20 - 3 = 17 • Mode: The mark that appears most frequently. Mode = 10 • Interquartile Range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1). Q1 is the median of the lower half of the data (3, 5, 10, 10, 11), so Q1 = 10. Q3 is the median of the upper half of the data (12, 14, 16, 19, 20), so Q3 = 16. IQR = Q3 - Q1 = 16 - 10 = 6 Thandiwe's results: Mean = 12, Median = 11.5, Range = 17, Mode = 10, IQR = 6. Step 2: Calculate for Anna's marks. There are n=10 marks. • Mean: Sum of marks divided by the number of marks. Mean = (11+11+11+12+12+12+12+13+13+13)/(10) = (120)/(10) = 12 • Median: The middle value of the sorted data. Since there are 10 marks, the median is the average of the 5th and 6th values. Median = (12+12)/(2) = (24)/(2) = 12 • Range: The difference between the highest and lowest marks. Range = 13 - 11 = 2 • Mode: The mark that appears most frequently. Mode = 12 • Interquartile Range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1). Q1 is the median of the lower half of the data (11, 11, 11, 12, 12), so Q1 = 11. Q3 is the median of the upper half of the data (12, 12, 13, 13, 13), so Q3 = 13. IQR = Q3 - Q1 = 13 - 11 = 2 Anna's results: Mean = 12, Median = 12, Range = 2, Mode = 12, IQR = 2. b) Which marks are better between Thandiwe's marks and Anna's marks? Give a reason for your answer. Anna's marks are better. Reason: While both students have the same mean mark of 12, Anna's marks are more consistent. Her range (2) and interquartile range (2) are significantly smaller than Thandiwe's range (17) and IQR (6). This indicates that Anna consistently scores around the average, whereas Thandiwe's scores vary widely, including some very low marks. Send me the next one 📸