Midterm Cheat Sheet

Midterm Cheat Sheet - Statistics a science that deals with...

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Statistics – a science that deals with the methods of collecting, organizing, and summarizing data in such a way that valid conclusions can be drawn from them. NOT: selecting the right data to support a hypothesis Descriptive Statistics – collecting, organizing, summarizing Inferential Statistics – analyzing, making decisions Parameter – characteristic of population Statistic – characteristic measure of sample Nominal scale – single, married, divorced (qualitative) Ordinal scale – good, neutral, bad (qualitative) Interval scale – no meaning of multiplication, no zero point (Fahrenheit temp, point scale) (quantitative) Ratio scale – multiplication of number has a meaning, zero point (temp on absolute scale, height) (quantitative) Quantitative data – measurement scale is numerical Qualitative data – measurement scale is categorical Discrete data – possible values are countable (1, 2, 3) Continuous data – infinite (1.1, 1.01, 1.001, 1.0001) FREQUENCY DISTRIBUTION Range Range = largest value – smallest value Sturges’s Rule Number of classes = 1 + 3.322 [log 10 (n)] n = number of data values (usually 5 – 15) Class Width/Size/Interval Width = largest value – smallest value / number of classes (always round up) Frequency Histogram – a bar graph, gap width = 0 NO GAPS Frequency Polygon – line graph of frequency distribution Classes Frequency Relative Frequency 0 – 1 44 44/76 = 58% Modal Class 2 – 3 25 25/76 = 33% 4 – 5 5 5/76 = 7% 6 – 7 1 1/76 = 1% 8 – 9 0 0/76 = 0% 10 – 11 0 0/76 = 0% 12 + 1 1/76 = 1% n = ∑f = 76 = 100% Probability – the chance that an event will occur. Will be a value from 0 to 1. 0 means the event will not occur, 1 means it definitely will. Anything between 0 and 1 represents the uncertainty of the event occurring. Mutually Exclusive Events – the occurrence of one does not allow for the occurrence of the other Independent Events – the occurrence of one event in no way influences the probability of the other occurring Relative Frequency of Occurrence Relative Frequency of Event = Number of times Event occurs / number of trials
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RULES OF PROBABILITY 1. 0 ≤ P (E) ≤ 1 2. P (S) = 1 probability for all events = 1 3. if A and B are mutually exclusive events, then: P (A or B) = P (A) + P (B) P (A and B) = 0 4. if A and B are NOT mutually exclusive, then: Addition Rule Theorem : P (A or B) = P (A) + P (B) – P (A and B) 5. P (Ø) = 0 probability of the empty set (impossible event) occurring 6. P (A’) = 1 – P (A) Example: A single fair die is thrown. Find the probability assigned to each of the events A, B, C, D A = {odd number appears} 1, 3, 5 B = {even number appears} 2, 4, 6 C = {number less than 4 appears} 1, 2, 3 D = {number greater than 2 appears} 3, 4, 5, 6 a) P (A and B) = 0 = {} mutually exclusive b) P (A or B) = 1 c) P (C)’ = 1 – P (C) = 1 – 3/6 = 0.5 d) P (C and D) = 1/6 e) P (C or D) = 1 Example: the following contingency table shows the number of students in business college for the year 1991- 92 distributed by age and gender Age B B’ Gender Under 20 20 or Older Total A Male 1500 2250 3750 A’ Female 1750 1850 3600 3250 4100 7350
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