Question

78. Suppose that the measurements of arm span and height

were converted from centimeters to meters by dividing
each measurement by 100. How will this conversion
affect the values of r² and s?
(a) ² will increase, s will increase.
(b)r will increase, s will stay the same.
(c) ² will increase, s will decrease.
(d) r² will stay the same, s will stay the same.
(e)r will stay the same, s will decrease.

Answer 1

Converting centimeters to meters by dividing by 100 will not affect the correlation coefficient (r) or the standard deviation (s).

Step-by-step explanation:

When converting the measurements from centimeters to meters, both the arm span and height values will be divided by 100. This means that the actual numerical values will decrease, but the relationship between the two measurements will remain the same.

In terms of correlation coefficient (r), the conversion will not affect its value as it only measures the strength and direction of the linear relationship between the two variables. Therefore, r will stay the same.

The standard deviation (s) measures the variability or spread of the data. Since dividing both measurements by the same constant does not change the spread of the data, s will also stay the same after the conversion.

Learn more about Effect of converting measurements from centimeters to meters on correlation coefficient and standard deviation