Introduction

Describing a score in relation to a distribution

• Knowing a score give little information without knowing where it is placed in the distribution.
• Knowing the mean of the distribution allows us to tell if a score is above or below the average.
• An individual scores 26 on a leadership test.
  • What does that mean? Are they a good leader or a bad leader?
  • If the mean of the test is 20, then we know that the person is above average in leadership (compared to others who have taken the test).

Example 1

• Knowing the standard deviation allows us to tell how much above or below the mean that score is in relations to the spread of the distribution.
• Leadership test:
• The person with the score of 26 is two standard deviations above the mean.

Example 2

• Planning Ability
• A person scores 84 on a test of planning ability.
• If , this person's score is 0.5 standard deviations below the mean.
• Thus the person is below average, but not by a lot.

Planning ability:

We can visualize that the score of 84 would be slightly lower than the mean.

Examples 3 and 4

• A person scores 114 on the test of planning ability.
  • If , this person's score is 2 standard deviations above the mean.
• Thus the person is above average by quite a bit.
• What if a person scored 78?
  • Then the person is below the average by about the average amount that scores deviated from the mean.
• Recall, standard deviation is the average amount the scores deviated from the mean.

Planning ability:

Visualize the score of 114 as far above the mean, while the score of 78 would be slightly below the mean.