10.x. Variance and Standard Deviation

Try these first

1. 1.

   Calculate the mean of the following data: 6, 2, 9, 5, 3.

   Hint

   Add the numbers together and divide by how many data points there are.

2. 2.

   True or False: The standard deviation can be negative.

   Hint

   Think about how we define standard deviation.

3. 3.

   What does variance measure?

   • Data average
   • Data spread from the mean
   • Data count

   Hint

   Think of how variance relates to the average value of data points.

4. 4.

   True or False: Standard deviation is simply a squared measurement of variance.

   • True
   • False

   Hint

   Consider the definition of standard deviation regarding variance.

5. 5.

   You collected the following set of data: 5, 7, 5, 8, 12. Calculate the variance and standard deviation, and discuss the implications of these measurements.

   Hint

   Go step-by-step, calculating the mean first, then varied deviations.

6. 6.

   Consider two sets of data: Set A: {6, 7, 8}, Set B: {2, 11, 12}. Calculate the variances for both sets and summarize differences in variability.

   Hint

   Remember to find the mean for each set then calculate the squared differences.