Question

Four persons have weights $50$ lb, $50$ lb, $45$ lb and $45$ lb. The average weight of four persons is .

• A. $44\text{lb}$
• B. $49\text{lb}$
• C. $47.5\text{lb}$

Answer 1

The correct option is C $47.5\text{lb}$

The given data set for the weights of four persons $\{50,50,45,45\}$.

The given data set can be represented using frequency table as

Weight (in lb)	Frequency
$50\left(x_1\right)$	$2\left(w_1\right)$
$45\left(x_2\right)$	$2\left(w_2\right)$

In the above table, frequency represents the number of people having the weights $50$ lb and $45$ lb. And those frequencies $(2,2)$ actually the denote the weighted factors $(w_1,w_2)$, and $(50\text{lb},45\text{lb})$ denote the data points $(x_1,x_2)$.

$\therefore$ Average weight of four persons

$=\frac{(w_1\times x_1)+(w_2\times x_2)}{(w_1+w_2)}$

$=\frac{(2\times 50)+(2\times 45)}{2+2}$

$=\frac{190}{4}=47.5\text{lb}$

$\therefore$ The average weight of four persons is $47.5$ lb.