10.x.3. Standard Deviation

Try these first

1. 1.

   What is the formula for standard deviation?

   Hint

   Think about how standard deviation relates to variance.

2. 2.

   Why is standard deviation preferable over variance?

   Hint

   Consider the implications of units in interpretation.

3. 3.

   What does a high standard deviation indicate?

   • Data points are close to the mean
   • Data points are spread out
   • Data points are negatively skewed

   Hint

   Think about the distribution of values.

4. 4.

   True or False: Standard deviation can be negative.

   • True
   • False

   Hint

   Consider what SD represents and the significance of distance.

5. 5.

   You collect the heights of five basketball players: 180 cm, 190 cm, 185 cm, 175 cm, and 195 cm. Calculate the variance and standard deviation of their heights.

   Hint

   First, find the mean, then calculate squared differences and their average.

6. 6.

   In a statistical experiment, the weights of bats are recorded as: 2.0 kg, 2.5 kg, 2.4 kg, and 3.0 kg. If the standard deviation is computed to be 0.3 kg, discuss how this affects the consistency of bat weights.

   Hint

   Reflect on what standard deviation tells us about the range of weights.