Question

The refractive index of glass is found to have the value 1.49, 1.50, 1.52, 1.54, and 1.48 the mean absolute error is​

Answer 1

The refractive index of glass is found to have the value 1.49, 1.50, 1.52, 1.54, and 1.48.

We have to find the mean absolute error.

Total number of rbservations are 5.

Now,

Mean = (Sum of all Observations)/(Total number of Observations)

Substitute the values in the above formula,

= (x₁ + x₂ + x₃ + x₄ + x₅)/5

= (1.49 + 1.50 + 1.52 + 1.54 + 1.48)/5

= 7.53/5

= 1.506

= 1.51 (approx.)

For Absolute Error:

x₁ = |1.49 - 1.51| = |-0.02| = 0.02

x₂ = |1.50 - 1.51| = |-0.01| = 0.01

x₃ = |1.52 - 1.51| = 0.01

x₄ = |1.54 - 1.51| = 0.03

x₅ = |1.48 - 1.51| = |- 0.03| = 0.03

So, Mean Absolute Error (Δx)  = (x₁ + x₂ + x₃ + x₄ + x₅)/5

Substitute the values,

= (0.02 + 0.01 + 0.01 + 0.03 + 0.03)/5

= 0.10/5

= 0.02

Therefore, the mean absolute error is 0.02.

Answer 2

Answer:

YOUR QUESTION :

The refractive index of glass is found to have the value 1.49, 1.50, 1.52, 1.54, and 1.48 the mean absolute error is

SOLUTION :

Mean value = sum of observations /number of observations

= (1.49 + 1.50 + 1.52 + 1.54 + 1.48)/5

= (7.53)/5

= 1.506 ≈ 1.50

Now, absolute error,

y₁ = |1.49 - 1.50| = 0.01

y₂ = |1.50 - 1.50| = 0.00

y₃ = |1.52 - 1.50| = 0.02

y₄ = |1.54 - 1.50| = 0.04

y₅ = |1.48 - 1.50| = 0.02

Now, mean absolute error = (y₁ + y₂ + y₃ + y₄ + y₅)/5

= (0.01 + 0.00 + 0.02 + 0.04 + 0.02)/5

= 0.09/5 = 0.018

∵ Relative error = Mean absolute error/mean value

= 0.018/1.50

= 0.012

Now, % error in the measurement =

100 × relative error = 100 × 0.012 = 1.2%