Question

janna is making a prediction of the frequency of a key that is 12 keys from middle c.
sound frequencies (piano)

number of keys above middle c	frequency (hz)
1	293.66
2	311.13
4	349.23
8	440.00

which best describes her prediction?

• interpolation, because a key that is 12 keys from middle c is within the data set
• interpolation, because a key that is 12 keys from middle c is outside the data set
• extrapolation, because a key that is 12 keys from middle c is within the data set
• extrapolation, because a key that is 12 keys from middle c is outside the data set

Explanation:

Interpolation is used for values within the data - set range, while extrapolation is for values outside. The data set has keys \(0,1,2,4,8\) above middle \(C\). A key \(12\) keys from middle \(C\) is outside this range (\(12>8\)). So, it is extrapolation.

Answer:

extrapolation, because a key that is 12 keys from middle C is outside the data set