1. Stat 100
Chapter 8, 1-3, 6-10
Read Chapter 9

2. What’s Wrong Here?

3. Pictogram Pictures used to represent a quantity within a group
Common Problem - picture distorts true relative sizes of quantities
In TCM ad, number of movies for TCM is about 1.5 times that of other channels, but
King Kong much more than 1.5 times as big as Shirley Temple

4. What’s Wrong?

5. Problem with Previous Graph
The lengths of the bars were not in scale.
Watch out for artistic stuff that distorts numerical axes.

6. Better Graph

7. Normal Curve
Symmetric bell-shaped curve that describes the likelihood that value occur
Mathematical model used to approximate the distribution of measurements in a population.

8. Percentiles for the Normal Curve
Table 8.1 on page 137 shows relationship between standardized scores and percentile ranks.
Any normal curve problem can be solved using this table.

9. Book’s Thought Quest. 2, Ch. 8
What does it mean to say that a man’s height is at the 30th percentile for all adult males?

10. Calculating Standardized Scores
“Formula” is z = (Value - Mean) / SD

11. Normal curve example
Amount that students slept last night has a mean of 7 hours and a standard deviation of 1.7
Assume a bell-shaped curve (normal curve) is appropriate

12. About what percent slept less than 5 hours?
Find standardized score for 5 hours.
Z=(57)/1.7 =  1.18
Look up percentile rank for z= 1.18 in table. Value given is about 12
About 12% slept less than 5 hours

13. What percent slept more than 10 hours?
Standardized score = (107)/1.7 = 1.76
Look up z=1.76. Closest z in table is 1.75
This is 96th percentile.
Answer =100%-96% = 4%

14. What percent slept between 5 and 10 hours?
Answer = 96%  12% = 84%
This is the difference in percentile ranks for 10 hours and 5 hours

15. What value of sleep is the 60th percentile?
Look for 60 under “Percentile” in table.
Corresponding z is z = 0.25.
What value of sleep has z = 0.25?
(0.25)(S.D) = (0.25)(1.7)  0.4
Answer = mean = = 7.4 hours