Question

if a sample consists of the following data values, what is the sample mean? 13, 91, 44, 28, 54, 16, 88, 74 a. 46 b. 56 c. 51 d. 41

Explanation:

Step1: Sum the data values

We add up all the given data values: \(13 + 91 + 44 + 28 + 54 + 16 + 88 + 74\). Let's calculate that: \(13+91 = 104\), \(104 + 44 = 148\), \(148 + 28 = 176\), \(176 + 54 = 230\), \(230 + 16 = 246\), \(246 + 88 = 334\), \(334 + 74 = 408\). So the sum of the data values is \(408\).

Step2: Count the number of data points

There are 8 data values in the sample (13, 91, 44, 28, 54, 16, 88, 74).

Step3: Calculate the sample mean

The formula for the sample mean \(\bar{x}\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(\sum_{i = 1}^{n}x_{i}\) is the sum of the data values and \(n\) is the number of data points. Substituting the values we found: \(\bar{x}=\frac{408}{8}=51\).

Answer:

C. 51