Grade 8 Scatter Plots: Correlation

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   x = x · y = y

   Data: x (x) and y (y)

   x	1	2	3	4
   y	55	58	57	50
   x	5	6	7	8
   y	48	51	48	41

   What type of association does the scatter plot show between the x-values and the y-values?

   1. Read the points from left to right (x from 1 to 8). Their y-values are 55, 58, 57, 50, 48, 51, 48, 41.
   2. Overall they go down: from 55 on the left to 41 on the right. As x increases, y tends to decrease.
   3. When both go in opposite directions, the association is negative.

   Answer: negative

2. Example 2

   x = Letters in first name · y = Minutes to school

   Data: Letters in first name (x) and Minutes to school (y)

   x	3	4	5	6
   y	5	22	9	8
   x	7	8	9	10
   y	25	7	20	6

   What type of association does the scatter plot show between the number of letters in a first name and the minutes to get to school?

   1. Read the points from left to right (x from 3 to 10). Their y-values are 5, 22, 9, 8, 25, 7, 20, 6.
   2. The y-values jump up and down with no steady direction: the lowest, 5, is at x = 3 and the highest, 25, is at x = 7. Knowing x doesn't tell you whether y is high or low.
   3. So the scatter plot shows no association.

   Answer: no association

3. Example 3

   x = Day of month born · y = Height (inches)

   Data: Day of month born (x) and Height (inches) (y)

   x	2	6	10	14
   y	56	62	63	62
   x	18	22	26	30
   y	66	65	65	55

   What type of association does the scatter plot show between the day of the month born and the height?

   1. Read the points from left to right (x from 2 to 30). Their y-values are 56, 62, 63, 62, 66, 65, 65, 55.
   2. The y-values jump up and down with no steady direction: the lowest, 55, is at x = 30 and the highest, 66, is at x = 18. Knowing x doesn't tell you whether y is high or low.
   3. So the scatter plot shows no association.

   Answer: no association