ECO 045 Exam 1 Study Guide PDF

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Chapter 1 Descriptive statistics- describes large amounts of data concisely Inferential statistics- drawing conclusions about an entire population from a small sample Categorical- can be grouped by specific categories, labels, and names Quantitative- uses numeric values ↳ Discrete - only certain values (ex. family size) ↳ Continuous - gets increasingly more precise (ex. height) Nominal- qualitative data Ordinal- order is meaningful (ex. rating 1-5) Interval scale- distance between values is meaningful and measurable (ex. 32°F is not half as cold as 64°F) Ratio scale- distance can be used to compare (ex. 50K salary is 2x as much money as 25K)

Mean- average value Median- middle value Mode- most frequently occurring value Frequency distribution- shows frequency of observations ↳ Relative  frequency- fraction or proportion of the total number, should all add up to 1 ↳ Relative  % frequency - relative frequency as a % (multiply x 100) ↳ Cumulative  frequency- number of items with values less than or equal to the upper limit of each class

Frequency

Relative Frequency

Relative % Frequency

Cumulative % Frequency

Bear

17

.18

18%

18%

Card

8

.09

9%

27%

Chocolate

42

.46

46%

73%

Wine

25

.27

27%

100%

Total

92

1

100%

Chapter 2 Categorical Data ↳ Frequency distribution ↳ Relative frequency distribution ↳ % frequency distribution ↳ Bar chart ↳ Pie Chart Pareto diagram- when bar chart bars are arranged in descending order of height left to right Qualitative Data ↳ Frequency distribution ↳ Relative frequency distribution ↳ % frequency distribution ↳ Cumulative distribution ↳ Histogram When creating a distribution, determine: 1. # of non-overlapping categories 2. Width of each class 3. Class limits

width =

largest data value − smallest # of classes

Open end class- requires only upper or lower class limit (ex. grades 60 or less)

Kurtosis- length of tails Spread- minimum value minus maximum value Cross tabulation - summarizes data for two variables, can be used with both qualitative and quantitative data

Side by side bars

Stacked bars

Trend Lines

Scatterplots and Correlations

Chapter 3 Population parameters - measures computed data from a population Sample statistic- measures computed data from a sample

Mean Variance Standard Deviation

Sample

Population

x

μ

S

2

S

σ

2

σ

Trimmed mean- remove smallest and largest values Weighted mean- more value/weight given to some values (ex. 3 vs 4 credit classes and GPA)

Geometric mean- used to analyze growth rates to determine mean rate of change

√(x1)(x2)...(xn) n

Quartiles- puts percentiles into four groups of 25% Deciles- puts percentiles into ten groups of 10% Percentile calculation-

p

i = ( 100 )n + 1

  = number of values i =  value at p percentile n

IQR- middle 50% Variance- s2

=

Σ(x−x) 2 or n−1

Standard deviation-

σ2 =

Σ(x−μ) 2 N

√s2

Coefficient of variance-

( sx x 100)%

or

( μσ x 100)%

Normal Distribution ↳ Mean = median = mode ↳ Skewness = 0 Z-score - number of standard deviations from the mean

x−μ σ or

x−x s

Empirical Rule- version of Chebyshev’s Theorem for Normal distribution ↳ 68.26% within 1 SD ↳ 95.44% within 2 SD ↳ 99.72% within 3 SD Outlier- more than 3 SD off from the mean Covariance- linear association between two variables ↳ between -1 and 1 ↳ more extreme = stronger

sxy =

Σ (xi −x)(yi −y) or n−1

σ xy =

Σ (xi−μ x)(y i−μ y ) n−1

Chapter 4 Experiment- chance process (ex. flip a coin) Event- outcome of a chance process (ex. coin lands on heads) Sample space- all possible outcomes of a chance process Probability- numerical likelihood 0-1 Types of Experiments ↳ Classical  - each outcome is equally possible, probability is number of successes divided by total outcomes ∞

↳ Relative  frequency- limit of relative frequency as # of trials gets larger

∫

0

s n

↳ Subjective  - degree of confidence or rational belief

Types of Events ↳ Simple  (ex. rolling two dice that add up to 2) vs compoundevents (ex. rolling two dice that add up to 7) ↳ Mutually  exclusive- if one event happens, another can’t, P(A∩B) = 0 ↳ Statistically  independent- one event has no effect on the other, P(A) = P(A|B) ↳ Complementary  - both events cannot happen but one will, P(A∩B) = 0 and P(A ⋃B) = 1

Symbol

Meaning

P(A)

Probability A will happen

P(Ā)

Probability A will not happen

P(A|B)

Probability A will happen given B happens

P(A’)

Probability the complement of A will happen

P(A∩B)

Probability A and B will both happen

P(A ⋃B)

Probability A or B will happen

P(A ⋃B) = P(A) + P(B) - P(A∩B) P(A∩B) = P(B) * P(A|B) or P(A) * P(B) when A and B are statistically independent

P(A|B) =

P (A∩B) P (B )...