Question

find the mean for the following group of data items.
5, 1, 4, 7, 6, 2, 1, 8
the mean is \boxed{}. (type an integer or a decimal.)

Explanation:

Step1: Sum the data items

We add up all the numbers: \(5 + 1 + 4 + 7 + 6 + 2 + 1 + 8\). Let's calculate that: \(5+1 = 6\), \(6+4 = 10\), \(10+7 = 17\), \(17+6 = 23\), \(23+2 = 25\), \(25+1 = 26\), \(26+8 = 34\). So the sum is \(34\).

Step2: Count the number of data items

There are 8 numbers in the list: 5, 1, 4, 7, 6, 2, 1, 8. So the count \(n = 8\).

Step3: Calculate the mean

The formula for the mean \(\bar{x}\) is \(\frac{\text{Sum of data items}}{\text{Number of data items}}\). So we divide the sum by the count: \(\frac{34}{8}=4.25\).

Answer:

\(4.25\)