Question

find the mean, $overline{x}$, of the data.
15, 21, 46, 49, 31, 24
$overline{x} = ?$

Explanation:

Step1: Sum the data values

To find the mean, we first sum all the data points. The data is \(15, 21, 46, 49, 31, 24\). So we calculate \(15 + 21 + 46 + 49 + 31 + 24\). Let's add them step by step: \(15+21 = 36\), \(36+46 = 82\), \(82+49 = 131\), \(131+31 = 162\), \(162+24 = 186\). So the sum of the data is \(186\).

Step2: Divide by the number of data points

The number of data points \(n\) is \(6\) (since there are 6 numbers: 15, 21, 46, 49, 31, 24). The formula for the mean \(\overline{X}\) is \(\overline{X}=\frac{\text{Sum of data}}{n}\). So we divide the sum (\(186\)) by \(n = 6\), which is \(\frac{186}{6}=31\).

Answer:

\(31\)