Question 1083730: 2. The table below shows data on 10 plants. They were planted in areas such that each plant received different amounts of direct sunlight on average per day. Each plant was planted on the same day and the data was collected on the same day.
Plant 1 2 3 4 5 6 7 8 9 10
Height (cm) 19 21 24 23 26 28 25 30 29 32
Average sunlight (hrs) 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5
(i) Represent the plant height on a stem and leaf plot.
(ii) Plot this data on a scatter diagram with height on the y-axis and average sunlight on the x-axis.
(iii) Calculate the correlation coefficient r. (iv) What does the r value suggest?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part (i)
The stems are the tens digits. The stems will be 1, 2 and 3.
The leaves are the units digits.
Here's what the stem and leaf plot looks like
See this page for guidance on a similar example if you're still stuck.
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Part (ii)
I'm using GeoGebra (free graphing software) to plot the scatter diagram.
This is the result I get
The points are
A = (8, 19)
B = (8.5, 21)
C = (9, 24)
D = (9.5, 23)
E = (10, 26)
F = (10.5, 28)
G = (11, 25)
H = (11.5, 30)
I = (12, 29)
J = (12.5, 32)
where x = average number of hours in the sunlight, y = height of plant
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Part (iii)
Using GeoGebra, I get the correlation coefficient to be approximately r = 0.9418
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Part (iv)
This r value of r = 0.9418 is very close to 1.00 which is to be expected since the data points in part (ii) all clump together closely. A regression line is a good fit for this data. There is a strong positive correlation.
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