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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.

Are there any outliers in the data shown on the scatterplot? If so, where?

(1 point)
Responses

Yes, at (65, 205)
Yes, at left parenthesis 65 comma 205 right parenthesis

Yes, at (74, 240)
Yes, at left parenthesis 74 comma 240 right parenthesis

Yes, at (74, 200)
Yes, at left parenthesis 74 comma 200 right parenthesis

No, there are no outliers in the data.

1 answer

To determine whether there are any outliers in the data shown in the scatterplot, we can analyze the distribution of the plotted points.

The points are:

  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)

By examining the y-values for each given x-value, we find that:

  • For x=65, the y-value is 205.
  • For x=67, the y-value is 216.
  • For x=68, the y-values are 210 and 218.
  • For x=69, the y-value is 224.
  • For x=70, the y-values are 220 and 224.
  • For x=71, the y-value is 230.
  • For x=72, the y-value is 235.
  • For x=74, the y-values are 200 and 240.

The points at (74, 200) and (74, 240) behave differently compared to the other points, which have y-values generally increasing as x increases. Specifically, the point (74, 200) is much lower than the other points plotted at or near x=74.

The analysis suggests that both (74, 200) and (74, 240) are potential outliers, but particularly (74, 200) stands out significantly because it is not consistent with the trend of increasing values.

Therefore, the presence of outlier(s) suggests:

Yes, at (74, 200)
Yes, at left parenthesis 74 comma 200 right parenthesis