Question

1. Can you identify the more heterogeneous group given an SD value of two groups? Can you identify which group as the greater degree of dispersion based on the standard deviation? Can you identify which group has more variability? Can you identify which group is more consistent based on SD?

2. If a z score is +1, what is the corresponding raw score value? If a z score is 0, what is the corresponding raw score value? If a raw score has a mean of 25, what is the corresponding z score value?

3. What happens to the area between +/- 1 SD as the standard deviation of a normal distribution increases?

4. Why are IQ scores normally distributed?

Answer 1

1. Group with larger SD has greater degree of dispersion. Hence Group with larger SD has more variability. Group with smaller SD is more consistent.

2. If z score=1 then corresponding raw score=mean+SD

If z score=0 then corresponding raw score=mean

z score when mean of raw score is 25=(raw score-25)/SD

3. The area between +/- 1 SD as the standard deviation of a normal distribution increases means SD increases hence the variability of the data increases.

4. IQ scores have a bell shaped distribution in the general population with an average IQ of 100. This curve has a peak in the middle where most people score and tapering ends where only a few people score. Hence we can assume IQ scores are normally distributed (since normal distribution is bell shaped distribution)