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An illustration of a scatterplot shows x on x-axis from 65 to 75 in increments of 1 and y on the y-axis from 200 to 240 in increments of 2.5. Eleven points are plotted. The approximate plotted points are as follows: left parenthesis 65 comma 205 right parenthesis, left parenthesis 67 comma 216 right parenthesis, left parenthesis 68 comma 210 right parenthesis, left parenthesis 68 comma 218 right parenthesis, left parenthesis 69 comma 224 right parenthesis, left parenthesis 70 comma 220 right parenthesis, left parenthesis 70 comma 224 right parenthesis, left parenthesis 71 comma 230 right parenthesis, left parenthesis 72 comma 235 right parenthesis, left parenthesis 74 comma 200 right parenthesis, and left parenthesis 74 comma 240 right parenthesis. "

is there a relationship beteween the two sets of data? how do you know?

yes becase the data points are close to the trend line
no because the data points are not close to the trend line
no because the data points are close to the trend line
yes because the data points are not close to the trend line

1 answer

To determine whether there is a relationship between the two sets of data based on the scatterplot description, we need to consider how the data points are distributed in relation to a potential trend line.

From the provided points:

  1. (65, 205)
  2. (67, 216)
  3. (68, 210)
  4. (68, 218)
  5. (69, 224)
  6. (70, 220)
  7. (70, 224)
  8. (71, 230)
  9. (72, 235)
  10. (74, 200)
  11. (74, 240)

To assess the relationship:

  • Most of the points seem to cluster around the middle values—this suggests a certain trend, particularly as x increases, y appears to increase overall, although there are outliers such as (74, 200).
  • The overall trend suggests that as x increases from 65 to 75, y also tends to increase, indicating a positive relationship.

Given this analysis, based on the options provided, the correct choice that aligns with the observation of the data points' distribution is:

Yes, because the data points are close to the trend line.

This option acknowledges that there appears to be some positive correlation as x increases y seems to increase for most of the plotted points.