Question

The length of a rod as measured in an experiment is found to be 2.48 m, 2.46 m, 2.49 m, 2.49 m and 2.46 m. Find its average length, the absolute error in each observation and the percentage error.

$\rule{200}2$

No spam.​

Answer 1

SoluTion:

We know that,

Average length = Arithmetic mean of the measured value

$\sf{x_{mean}\:=\:\dfrac{2.48+2.46+2.49+2.49+2.46}{5}}$

$\longrightarrow$ $\sf{x_{mean}\:=\:\dfrac{12.38}{5}}$

$\longrightarrow$ $\sf{x_{mean}\:=\:2.48\:m}$

Hence, True value = 2.48 m.

Absolute errors in various measurements :

|∆x1| = |x1 - x_mean|

$\longrightarrow$ 2.48 - 2.48

$\longrightarrow$ 0.00 m

|∆x2| = |2.46 - 2.48|

$\longrightarrow$ 0.02 m

|∆x3| = |2.49 - 2.48|

$\longrightarrow$ 0.01 m

|∆x4| = |2.49 - 2.48|

$\longrightarrow$ 0.01 m

|∆x5| = |2.46 - 2.48|

$\longrightarrow$ +0.02 m

Mean absolute error :

$\longrightarrow$ $\sf{\dfrac{|\Delta x_{1}| + |\Delta x_{2}| + ... + |\Delta x_{5}|}{5}}$

$\longrightarrow$ $\sf{\dfrac{0.00+0.02+0.01+0.01+.0.02}{5}}$

$\longrightarrow$ $\sf{\dfrac{0.06}{5}}$

$\sf{\Delta x_{mean} = 0.01\:m}$

Therefore,

• x = 2.48 ± 0.01 m

Now, percentage error :

$\longrightarrow$ $\sf{\dfrac{\Delta x_{mean}}{x} \times 100}$

$\longrightarrow$ $\sf{\dfrac{0.01}{2.48} \times 100}$

$\longrightarrow$ 0.40 %

Answer 2

Answer:

(2.48 + 2.46 + 2.49 + 2.50 + 2.48)/5 =2.482.

Step-by-step explanation:

Please mark me as brainliest please please please