1.3 Visualizing Trends In Data

The given graph shows a strong negative correlation. This means that as one variable increases, the other variable decreases at a strong rate. The data points on the graph are closely clustered in a downward sloping pattern, indicating a strong negative relationship between the two variables.

The graph indicates a weak positive correlation, meaning that there is a slight upward trend in the relationship between the variables. As one variable increases, the other variable also tends to increase, but the relationship is not very strong.

The statement suggests that there is no correlation between student height and grade in mathematics. This means that there is no consistent relationship between these two variables. In other words, knowing a student's height does not provide any information about their grade in mathematics, and vice versa.

The given correct answer suggests that there is a positive correlation between the amount of time spent studying for a math test and the mark achieved. This means that as the amount of time spent studying increases, the mark achieved also tends to increase. In other words, students who spend more time studying for the math test are more likely to achieve higher marks.

A line of best fit represents the trend of the data. It is a line that is drawn on a scatter plot to show the general direction or pattern of the data points. The line is placed in such a way that it minimizes the overall distance between the line and the data points. This helps to identify any underlying relationship or trend between the variables being plotted. The line of best fit does not necessarily have to pass through the origin, the median of the data, or have a positive slope. It is simply a tool to visually represent the overall trend in the data.

The statement "the trend of the data exhibits an irregular decline" is not true. A strong negative correlation means that as the independent variable increases, the dependent variable decreases consistently. Therefore, the trend of the data would exhibit a regular decline, not an irregular one.

A negative correlation would exist between the number of hotdogs that a vendor sells and the price charged per hotdog. This means that as the price charged per hotdog increases, the number of hotdogs sold would decrease. Conversely, if the price charged per hotdog decreases, the number of hotdogs sold would increase. This suggests that there is an inverse relationship between the two variables, indicating a negative correlation.