Question

find the mean, $overline{x}$, of the data.
465, 460, 497, 462, 462, 474
$overline{x} = ?$

Explanation:

Step1: Calculate the sum of the data

$$465 + 460+497 + 462+462+474$$
$$=(465 + 460)+497+(462 + 462)+474$$
$$=925+497 + 924+474$$
$$=(925+497)+(924 + 474)$$
$$=1422+1398$$
$$=2820$$

Step2: Calculate the number of data points

There are \(n = 6\) data points.

Step3: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Substitute \(\sum_{i=1}^{n}x_{i}=2820\) and \(n = 6\) into the formula: \(\bar{x}=\frac{2820}{6}=470\)

Answer:

\(470\)