7.7. Variance

Try these first

1. 1.

   Define variance in your own words.

   Hint

   Think about the average and how each number relates to it.

2. 2.

   What does a low variance indicate about a dataset?

   Hint

   Consider how tightly packed the values are.

3. 3.

   What does a higher variance indicate about a dataset?

   • More consistent values
   • More spread out values
   • Equal values

   Hint

   Consider what happens to the spread of values if they are all similar.

4. 4.

   True or False: High variance is always desirable in engineering.

   • True
   • False

   Hint

   Think about reliability in engineering processes.

5. 5.

   A factory produces metal rods that are supposed to be 5 cm in length. During testing, a sample produced lengths of {4.8, 5.1, 5.0, 4.9, 5.2} cm. Calculate the variance.

   Hint

   Calculate the mean, then find the squared differences from the mean.

6. 6.

   Analyze a given set of data points {1, 2, 3, 4, 5} and discuss how variance can impact product decisions in an engineering design.

   Hint

   Consider how this spread affects reliability and consistency.