1. Stat 1301 Percentiles and the Normal Distribution

2. 2-step Procedure
STEP 1: Convert data value to Standard Units (z-score)
Value - AVG z = SD
STEP 2: Find area (%) using normal curve

3. Converting z-score to its corresponding Value (in units of problem)
Value - AVG Z = SD so
Value = AVG + SD x Z

4. Recall Height Data AVG = 50 in. SD = 15 in. “Normal”
Standard Units Ht. (Inches)
Z = 1.5
Z = -2

5. IF data are NORMAL, the distribution is sufficiently described using
AVG SD
IF NON-NORMAL, these do not completely describe the distribution since distribution shapes may vary
- could use PERCENTILES

6. PERCENTILES
kth percentile - value below which k% of the distribution falls
(Note: Median = 50th percentile)
Methods of Finding Percentiles
1. From data (histogram, etc.)
2. Using Normal Curve (if appropriate)

7. BOX PLOTS - graphical presentation of percentile information
- Plot of minimum, maximum, along with 25th, 50th and 75th percentile
min th 50th th max

10. Calculating Percentiles From Normal Curve
Setting
- data NORMAL
- you know AVG and SD
STEPS:
1. Find z-score corresponding to desired percentile
2. Convert to units of the problem

12. IQ Data: - AVG = 114 - SD = 15 - “Normal”
Find 90th percentile
Find 25th percentile