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)
0 | 277.18
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 when predicting within the range of known data points. Extrapolation is used when predicting outside the range of known data points. Here, the data set has keys \(0,1,2,4,8\) above middle C. A key \(12\) keys from middle C is outside this data set. So it is extrapolation.

Answer:

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