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## STATS 200: Week 3 Notes

by: Alicia Polcha

22

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2

# STATS 200: Week 3 Notes STAT 200

Alicia Polcha
Penn State
GPA 4.0

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These notes will cover all of chapter 3 of what will be on the quiz for next week! Includes: Mean, mode, median, standard deviation, and variance.
COURSE
Elementary Statistics
PROF.
Prof. Justin Keller
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
Statistics, Math, Stats, Business Math, mean, average, standard deviation
KARMA
25 ?

## Popular in Statistics

This 2 page Class Notes was uploaded by Alicia Polcha on Saturday January 30, 2016. The Class Notes belongs to STAT 200 at Pennsylvania State University taught by Prof. Justin Keller in Spring 2016. Since its upload, it has received 22 views. For similar materials see Elementary Statistics in Statistics at Pennsylvania State University.

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Date Created: 01/30/16
Statistics: Chapter 3.1 1. Mean: average of a set of numbers a.  (sum of all data values) / (number of values) b.  Mean = (Σx) / (n) i. Let x be a quantitative variable with n measured data value from a  population of n. c. Example: i. 10, 15, 20, 25….625 ii. (n+1) / 2 iii. “n” : position of the middle number (n odd) between the position  of the two middle numbers  ( n even ) iv. Mean:  1. Sample Mean = x = Σx / n (statistic) 2. Population Mean =  μ =  Σx / n (parameter) 2. Median: Middle data value (the central value of an order distribution) a. Median = (sum of the values / 2) b. Example: i. 10, 14, 20, 8, 10, 16, 30, 12 ii. Put these numbers in order iii. 8, 10, 10, 12, 14, 16, 20, 30 iv. Median = (12 + 14) / 2 = 13 3. Mode: Most frequent data value (data value with highest frequency) a. Example: AAA BBB CC i. Since both A and B occur most equally, there is no mode of the  data  4. Detecing Skewness a. Symmetirical Distribution = mean ≈ median ≈ mode b. Left Skewed = mean < median < mode c. Right Skewed = mode < median < mean 5. Trimmed Mean a. 1, [1, 1, 1, 2, 2, 2, 3, 3, 3, 8, 9, 25, 26, 26, 26, 30, 50,] 100 b. n = 20 c. mean = (Σx) / 20 = 16 d. 5% trimmed mean: i. 0.05 x (20) = 1 (Remove highest and lowest ONE value) e. 10% trimmed mean: i. 0.1 x 20 = 2 (Remove highest and lowest two values) ii. (Σx) / 16 = 12.166 1. Chapter 3.2 Measures of Variation a. Mean: The mean gives us a way to describe an ‘average’ data value i. Consider these two data sets: ii. { 9 9 10 11 11 } { 0 5 10 15 20 } iii. Mean = (Σx) / (n) b. Range: a set of data is the difference between the high and low value i. Range = highest number – lowest number 1. Example 2. { 9 9 10 11 11 } 3. Range = 11 – 9 = 2 c. Variance: a sensitive measure of variation i. Sample Variance: is the quantity: 1. S  = [Σ (x – x(bar)) ] / n ­1 ii. Population Variance: is the quantity: 2 2  1. σ  = [Σ (x ­ μ ) ] / (N) d. Mean vs Variance i. Mean:  1. Population: μ 2. Sample: x(bar) ii. Variance: 1. Population: σ 2 2 2. Sample: S

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