Question 1: Bivariate data involves two variables plotted against each other on a scatter graph. Accurate plotting requires correct scaling and labeling. Errors in these areas can lead to misconceptions about the relationship between variables.

Answer: Errors in scaling or plotting points incorrectly can distort the data trend and lead to false conclusions.

Question 1: Plot the points (2, 3), (4, 7), and (6, 11) on the grid. Describe the pattern you observe.

Answer: Points form a straight line with slope 2, indicating a linear relationship.

Question 2: Identify the mistake in the following scatter plot: points show an increasing trend but are plotted with inconsistent scale on the y-axis.

Answer: The y-axis scale is inconsistent, causing misinterpretation of the trend.

Question 3: Calculate the correlation coefficient for the data points: (1,2), (2,4), (3,6), (4,8).

Answer: 1 (perfect positive correlation)

Question 4: A student plots data with an outlier that does not fit the overall trend. How might this affect the correlation coefficient and the interpretation?

Answer: The outlier may decrease the correlation coefficient, making the relationship seem weaker or non-linear.

Question 5: Construct a scatter graph to illustrate a positive linear relationship with some variability. Label the axes appropriately.

Answer: Students draw points roughly following a rising trend, with some scatter, and label axes accordingly.

Question 6: Explain why relying solely on visual inspection of a scatter plot can sometimes be misleading when assessing the strength of a relationship.

Answer: Because scatter plots can be affected by outliers, scale, or data density, visual assessment may overestimate or underestimate the strength of the relationship.

Question 7: Given the data points: (1, 5), (2, 7), (3, 9), (4, 11), identify the error if the points are plotted with the y-axis scaled from 0 to 10 instead of 0 to 15.

Answer: The y-axis scale is incorrect, leading to overlapping points and misrepresenting the data trend.

Question 8: Describe how a mislabeling of axes can influence the interpretation of a scatter graph.

Answer: Mislabeling axes can lead to incorrect conclusions about the relationship between variables, such as confusing cause and effect.

Question 9: Identify and correct the common mistake made when plotting the point (3, 4) as (4, 3). How does this affect the graph?

Answer: Swapping x and y coordinates misplaces the point, distorting the data pattern and possibly misleading trend analysis.

Question 10: In a scatter graph, explain why outliers should not be ignored without investigation.

Answer: Outliers may indicate data entry errors, variability in data, or a different underlying trend that requires further analysis.

Question 11: A student notices that the points on a scatter plot form a clear curved pattern rather than a straight line. How should this influence their interpretation?

Answer: The data suggests a non-linear relationship; a different model, such as quadratic or exponential, might be more appropriate.