Stat 1301 Percentiles and the Normal Distribution

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Presentation transcript:

Stat 1301 Percentiles and the Normal Distribution

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

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

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

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

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)

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

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

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