Question

A blood sample with a known glucose concentration of 102.0 mg/dL is used to test a new at home glucose monitor. The device is used to measure the glucose concentration in the blood sample five times. The measured glucose concentrations are 104.5 , 96.2 , 102.2 , 98.3 , and 101.8 mg/dL. Calculate the absolute error and relative error for each measurement made by the glucose monitor. A. 104.5 mg/dL absolute error = 2.5 mg / dL relative error = 0.025 B. 96.2 mg/dL absolute error = −5.8 mg / dL relative error = 0.057 C. 102.2 mg/dL absolute error = 0.2 mg / dL relative error = 0.020 D. 98.3 mg/dL absolute error = −3.7 mg / dL relative error = 0.036 E. 101.8 mg/dL absolute error = −0.2 mg / dL relative error =

Answer 1

The Absolute Error is the difference between the actual and measured value.

`Absolute \:error = |Actual \:value - Measured \:value|`

The Relative Error is the Absolute Error divided by the actual measurement.

`Relative \:error = (Absolute \:error)/(Actual \:value)`

We know that the actual value is 102.0 mg/dL.

To find the absolute error and relative error for each measurement made by the glucose monitor you must use the above definitions.

a) For a concentration of 104.5 mg/dL the absolute error and relative error are

`Absolute \:error = \left|102-104.5\right|\\Absolute \:error =\left|-2.5\right|\\Absolute \:error =2.5`

`Relative \:error = (2.5)/(102.0)=0.0245`

b) For a concentration of 96.2 mg/dL the absolute error and relative error are

`Absolute \:error = \left|102.0-96.2\right|\\Absolute \:error =\left|5.8\right|\\Absolute \:error =5.8`

`Relative \:error = (5.8)/(102.0)=0.0569`

c) For a concentration of 102.2 mg/dL the absolute error and relative error are

`Absolute \:error = \left|102.0-102.2\right|\\Absolute \:error =\left|-0.2\right|\\Absolute \:error =0.2`

`Relative \:error = (0.2)/(102.0)=0.00196`

d) For a concentration of 98.3 mg/dL the absolute error and relative error are

`Absolute \:error = \left|102.0-98.3\right|\\Absolute \:error =\left|3.7\right|\\Absolute \:error =3.7`

`Relative \:error = (3.7)/(102.0)=0.0363`

e) For a concentration of 101.8 mg/dL the absolute error and relative error are

`Absolute \:error = \left|102.0-101.8\right|\\Absolute \:error =\left|0.2\right|\\Absolute \:error =0.2`

`Relative \:error = (0.2)/(102.0)=0.00196`