Question

You are attempting question 1 out of 12
Determine the weighted mean for the observations of a distance are recorded as
472.15, 472.19, 472.22 and 472.20 and the relative weights to individual
observations are 1,2,3, and 2 by the land surveyor​

Answer 1

soryyyyyyyy............

Answer 2

Given:

The following observations of distance and the relative weights are given:

Distance observed:   472·15    472·19    472·22     472·20

Relative weights   :       1               2             3               2

To Find :

We have to find the weighted mean for the observation of the distance taken by the surveyor.

Solution:

The weighted mean of the observation is calculated by just multiplying the numbers in the observation by their relative weight and then add the numbers.

The formula can be written as follows:

                            $\[\mathop x\limits^\_ = \frac{{\sum\limits_{i = 1}^n {{x_i} \times {w_i}} }}{{\sum\limits_{i = 1}^n {{w_i}} }}\]$

where

$\[\mathop x\limits^\_ \]$ is the weighted mean

w is the weights

x is the value

The weighted mean of the observation of a distance ⇒

                           $\[\begin{array}{l}\mathop x\limits^\_ = \frac{{\left( {472 \cdot 15 \times 1} \right) + \left( {472 \cdot 19 \times 2} \right) + \left( {472 \cdot 22 \times 3} \right) + \left( {472 \cdot 15 \times 2} \right)}}{{(1 + 2 + 3 + 2)}}\\\\\,\,\,\,\, = 472 \cdot 198\end{array}\]$

∴ The weighted mean of the observation of a distance by the surveyor = 472·198.