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Students in Mrs. Anderson’s health class are learning about how exercise affects your heart rate. Twelve students ran around the school track for different lengths of time. Then they measured their heart rates in beats per minute.

Heart Rate Record
Minutes
Heart Rate
(bpm)
7
121
8
136
7
122
4
96
3
90
6
120
7
118
4
98
2
84
5
110
7
118
8
128
Find the correlation coefficient of the data. Round to the nearest hundredth.

1 Answer

6 votes

The correlation coefficient of the data about time and heart rate is 0.98.

How to calculate correlation coefficient?

We have been given time and heart rates of students in Mrs. Anderson's health class and we have to find the value of correlation coefficient.

The formula by Karl Pearson to calculate correlation coefficient is as under:

Correlation coefficient = ∑(x - x-bar) (y - y-bar))/(√[∑(x - x-bar)²]√[∑(y - y-bar)²]

We have to calculate figures required to fill in the formula which are:

∑(x-x bar)(y-y bar)=350

∑(x - x-bar)² = 44.67

∑(y - y-bar)² = 2872.25

Correlation coefficient=350/(√44.67 * √2872.25)

=350/6.68*53.59

=350/357.98

=0.977

After rounding off to nearest hundred it will be 0.98.

Hence the correlation coefficient of the data about time and heart rate is 0.98.

User Van Du Tran
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