1. Task 1: Interpretation of Data Representation Techniques (a) The researcher claims that a positive correlation always indicates a stronger relationship than a negative correlation. This statement is incorrect because the strength of a correlation is determined by the absolute value of the correlation coefficient, not its sign. For example, a correlation of -0.9 is stronger than a correlation of 0.5 because $|{-0.9}| = 0.9 > 0.5$. (b) A correlation of -0.85 between time spent on social media and GPA indicates a strong negative relationship. This means as time on social media increases, GPA tends to decrease significantly. (c) Changing the correlation from -0.92 to 0.92 reverses the direction of the relationship but keeps the strength the same. Originally, there was a strong negative correlation; after the change, there is a strong positive correlation, meaning the variables now increase together. (d) Two applications of correlation in education settings in Ginganni could be: 1. Examining the relationship between study hours and exam scores. 2. Investigating the link between attendance rates and academic performance. 2. Task 2: Analysis of Measures of Central Tendency and Variability Given data: 45, 50, 70, 45, 75, 80, 85, 55, 30, 60, 65, 65, 35 (a) Constructing a box and whisker plot: 1. Order data: 30, 35, 45, 45, 50, 55, 60, 65, 65, 70, 75, 80, 85 2. Minimum = 30 3. Maximum = 85 4. Median (middle value) = 60 (7th value) 5. Lower quartile (Q1) = median of lower half (30,35,45,45,50,55) = average of 45 and 45 = 45 6. Upper quartile (Q3) = median of upper half (60,65,65,70,75,80,85) = 70 (b) Calculate range, variance, and standard deviation: 1. Range = max - min = 85 - 30 = 55 2. Mean $\bar{x} = \frac{45+50+70+45+75+80+85+55+30+60+65+65+35}{13} = \frac{760}{13} \approx 58.46$ 3. Variance $s^2 = \frac{1}{n-1} \sum (x_i - \bar{x})^2$ Calculate squared deviations: $(45-58.46)^2=180.97$, $(50-58.46)^2=71.53$, $(70-58.46)^2=132.67$, $(45-58.46)^2=180.97$, $(75-58.46)^2=272.67$, $(80-58.46)^2=462.67$, $(85-58.46)^2=702.67$, $(55-58.46)^2=11.97$, $(30-58.46)^2=812.67$, $(60-58.46)^2=2.37$, $(65-58.46)^2=42.67$, $(65-58.46)^2=42.67$, $(35-58.46)^2=552.67$ Sum = 3,461.02 Variance $s^2 = \frac{3461.02}{12} \approx 288.42$ 4. Standard deviation $s = \sqrt{288.42} \approx 16.98$ Interpretation: - Range shows the spread between lowest and highest scores. - Variance and standard deviation measure how scores vary around the mean; higher values indicate more variability. (c) Reasons for measures in decision making: - Central tendency helps summarize typical performance to guide curriculum planning. - Variability informs about consistency of student performance, aiding targeted interventions.