1) The values \( 6,8,12 \), and 14 have an average of 10 . What is the average deviation? 12 3 3.65

To calculate the average deviation, we first find the deviations of each value from the average \(10\): - Deviation for \(6\) is \(10 - 6 = 4\) - Deviation for \(8\) is \(10 - 8 = 2\) - Deviation for \(12\) is \(12 - 10 = 2\) - Deviation for \(14\) is \(14 - 10 = 4\) Now we sum these deviations: \(4 + 2 + 2 + 4 = 12\). Finally, we divide the total deviation by the number of values \(4\): Average Deviation = \(\frac{12}{4} = 3\). So, the answer is \(3\). Now, let's spice things up! Did you know that the concept of average deviation can be linked back to early statistics around 18th century France? Mathematicians were keen on finding a better understanding of how values spread from a central point, which played a vital role in fields like economics and social sciences! And if you ever want to apply this knowledge, consider using average deviation when analyzing data for school projects or business reports. It's a great way to gauge not just what the average is, but how much variation there is from that average. Just remember, it's all about unearthing the hidden stories behind numbers!