Question

the mean of the data set { 3, 3, 4, 5, 7, 7, 8, 9, 11, 12 } is about ______. 10.010 6.90 7.00

Explanation:

Step1: Calculate the sum of the data set

First, we add up all the numbers in the data set: \(3 + 3 + 4 + 5 + 7 + 7 + 8 + 9 + 11 + 12\). Let's compute this step by step:
\(3 + 3 = 6\); \(6 + 4 = 10\); \(10 + 5 = 15\); \(15 + 7 = 22\); \(22 + 7 = 29\); \(29 + 8 = 37\); \(37 + 9 = 46\); \(46 + 11 = 57\); \(57 + 12 = 69\). So the sum of the data set is \(69\).

Step2: Determine the number of data points

The data set \(\{3, 3, 4, 5, 7, 7, 8, 9, 11, 12\}\) has \(10\) data points (we can count them: 3, 3, 4, 5, 7, 7, 8, 9, 11, 12 – that's 10 numbers).

Step3: Calculate the mean

The formula for the mean (\(\bar{x}\)) of a data set is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(\sum_{i = 1}^{n}x_{i}\) is the sum of the data points and \(n\) is the number of data points. We know the sum is \(69\) and \(n = 10\), so the mean is \(\frac{69}{10}=6.9\).

Answer:

6.90