Question

If the random error in 10 observation is x, then the
random error in 50 observation is
(1) x
(2) 3 x
(3)x/5
(4) 5x​

Answer 1

Explanation:

Error in 10 observation = x

Random error in 1 observation = x/10

Random error in 50 observation = x/10 ×50 Ans : 5x

Answer 2

Given:

The random error in 10 observation is x.

To Find:

The random error in 50 observation.

Solution:

We know that,

A chance discrepancy between the observed and true values of something is known as a random error.

Random error is a normal component of measurement and isn't always a mistake. Precision, which is how accurately the same measurement can be made again under similar conditions, is the main outcome of random error.

Compared to small samples, large samples have lower random error. This is because having more data points makes it easier to cancel out errors coming from different directions. Hence, we can say that random error is inversely proportional to the number of observations.

random error ∝ 1 / number of observations

Let y be the random error when the number of observations is 50.

Therefore,

$\frac{x}{y} = \frac{50}{10}$

$y = \frac{10}{50} x$

Hence, y = x/5.

Therefore, the random error in 50 observation is x/5. Option(3) is the correct answer.

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