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Unformatted text preview: SPARK CHARTS ™ Statistics page 1 of 4 This downloadable PDF copyright © 2004 by SparkNotes LLC. SPARK CHARTS TM STATISTICS SPARK CHARTS TM Copyright © 2002 by SparkNotes LLC. All rights reserved. SparkCharts is a registered trademark of SparkNotes LLC. A Barnes & Noble Publication 10 9 8 7 6 5 4 3 2 Printed in the USA $4.95 $7.95 CAN SPARK CHARTS TM 50495 9781586636364 I BN 1586636367 Instead of studying a large population of objects, individuals, or events, we often study a subset of the population called a sample. • Histogram: A pictorial representation of the frequency distribution of the observed sampled data • Sample mean: A measure of the central tendency of the data: x = x i n • Sample variance: A measure of the spread of the data: s 2 = ( x i − x ) 2 n − 1 • Sample standard deviation: s = √ s 2 • Range of sample: x max − x min • Mode of sample: The most frequently occurring value in a sample • Median of sample: The middle value (or average of the two middle values) when the data are ordered from smallest to largest • Quartiles (Q 25 , Q 50 , Q 75 ): Values that divide the ordered data into four parts of equal size • Interquartile range: Q 75 — Q 25 Definition: Events A and B are independent if the fact that one of them happened does not imply anything about the chance of the other one happening. Definition: Events A and B are mutually exclusive if they can’t happen at the same time: P ( A ∩ B ) = 0 . BASIC RULES OF PROBABILITY 1. ≤ P ( A ) ≤ 1 The probability of any event A is between and 1 . 2. P (not A ) = 1 − P ( A ) The probability that event A does not happen is one minus the probability that it does. 3a. If events A 1 , A 2 , A 3 , . . . are mutually exclusive, then P ( A 1 or A 2 or A 3 or . . . ) = P ( A 1 ∪ A 2 ∪ A 3 ∪ · · · ) = P ( A 1 ) + P ( A 2 ) + P ( A 3 ) + · · · . The probability that one of several mutually exclusive events happens is the sum of their probabilities. Example: The probability of rolling a die and getting a 1 or a 6 is 1 6 + 1 6 = 1 3 . 3b. P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) This is the probability that A or B or both occur. 4. If events A 1 , A 2 , A 3 , . . . are independent, then P ( A 1 and A 2 and A 3 and . . . ) = P ( A 1 ∩ A 2 ∩ A 3 ∩ · · · ) = P ( A 1 ) P ( A 2 ) P ( A 3 ) . . . Example: The probability of rolling a 1 and then a 6 is 1 6 × 1 6 = 1 36 . CONDITIONAL PROBABILITY Definition: The probability that event B will occur if you know that event A has already occurred is denoted P ( B  A ) and called the conditional probability of B given A . Multiplication rule: P ( A ∩ B ) = P ( B  A ) P ( A ) The probability of A and B is the probability of B given A times the probability of A ....
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This note was uploaded on 04/10/2008 for the course STAT 578 taught by Professor Kirnan during the Spring '07 term at Harvard.
 Spring '07
 Kirnan
 Statistics, Probability

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