MATH_2040_Chapter_4_Study_Guide Math 2040
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This 4 page Study Guide was uploaded by Ang Judd on Tuesday February 2, 2016. The Study Guide belongs to Math 2040 at Southern Utah University taught by Said Bahi in Winter 2016. Since its upload, it has received 22 views. For similar materials see Business Statistics in Math at Southern Utah University.
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Date Created: 02/02/16
Arithmetic (Simple) Mean ẍ=∑x n Weighted Mean ẍw= ∑(WXi i * Put the variable to weigh in the calculator first* ∑(Wi) !!!!X's FIRST!!!! Trimmed Mean ex)Find the 10% trimmed mean n=10 10% of n =10x 0.1 Remove one observation from each side Median n+1 2 Variation/Deviation ∑(x-ẍ) Mode Mode: The most frequent value (or observation) The Right Measure of Center Qualitative Quantitative Nominal Ordinal Interval Ratio Mean X X Median X X X Mode X X X X Trimmed Mean X X Moving Average *Used for time series* ex) Observing in time change in revenue for a business month return 2 period MA 3 period MA 1 5% 2 1% (5+1)/2 6% 3 3% (1+3)/2 2% (5+1+3)/3 3% 4 12% (3+12)/2 75% (1+3+12)/3 5% 5 11% (12+11)/2 11.50% (3+12+11)/3 8.60% 6 15% (11+15)/2 13% (12+11+15)/3 12.60% Range Range: The highest observation - the lowest observation Standard Deviation Sample Standard Deviation Population Standard Deviation 2 2 s=√ ∑ (x-ẍ) Ợ=√ ∑ (x-μ) n-1 n Variance Sample Variance Population Variance 2 2 2 2 s = ∑ (x-ẍ) Ợ = ∑ (x-ᵞ) n-1 n Mean Deviation ∑ l x-ẍ l n Empirical Rule: Use if the data set is symetrically bell shaped 68% of the values are within one standard deviation range: ẍ+/-sor μ+/-Ợ 95% of the values are withing two standard deviations range: ẍ+/-2s or μ+/-2Ợ 99.7% of the data values are within three standard deviations range: ẍ+/-3s or μ+/-3Ợ Chebysher's Rule: Use if the data is not bell shaped 2 1-1/k *k is the number of standard deviations* Finding the Percentiles L =n p L= location 100 n= sample size p= percentile we want Quartile Box Plot Q : L = n(25/100) 1 25 Q 2 L50 n(50/100) Q 3 L75 n(75/100) IQR IQR= Q 3Q 1 Box and Whisker Plot Steps 1) Order data 2) Put in minimum value and maximum value; Make sure you have even spacing 3) Plug in quartiles 4) Create a box over your number line 5) Add the whiskers to the minimum and maximum Outliers Upper Outlier: value > Q + 1.5(IQR) 3 Lower Outlier: value< 1 -1.5(IQR) Z-Scores population x-ᵞ sample x-ẍ Ợ s Coeffitcient of Variation Population CV= Ợ x100 Sample CV= S x100 ᵞ ẍ Finding the Mean of Grouped Data Sample Population ẍ= ∑(fx) μ= ∑(fx) ∑(f) ∑(f) Finding the Standard Deviation of Grouped Data Sample s=√ ∑(fx) Population Ợ=√ ∑(fx) ∑(f) ∑(n) Finding the Variation of Grouped Data Varience = s or =Ợ2 In the calculator X i1 L Weight/Frequency in2L FrequencyList i2 L Proportions Define the sample population Ṕ= x n (P- hat) Finding a Measure of Association Correlation r= 1 x ∑(x-ẍ)-(y-ÿ) n-1 (s )(s ) x y -1 ≤ r ≥ 1 -1 is a perfect negative correlation 0 is no linear correlation 1 is a perfect positive correlation
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