Statistics FInal Review: True/False/Uncertain Question 2

Q1, Q2, Q3, Q4: Finding Q2

2(N+1)/4

Q1, Q2, Q3, Q4: Finding Q3

3(N+1)/4

Mean Absolute Deviation

MAD = ∑Ixi-μI N

∑

summation sign

Comparison of Measures: Relative Sizes

symmetry and skewness

Standard Deviation: Definition

the (positive) square root of the variance

Median

the data value that has as many observations above it as below it

Range

the difference between the highest and lowest values

Interquartile Range

the difference between the third and first quartiles (Q3-Q1)

The Greater the Dispersion

the less useful are measures of central tendency

With Skewness, the Most Representative Measure of Central Tendency is:

the median

N

the number of data values in the population

n

the number of data values in the sample

Arithmetic Mean

the sum of the data values divided by the number of observations

Mode

the value that occurs with the greatest frequency (single, most typical value)

Comparison of Measures

usefulness and relative sizes

wi

weight given to the ith data value

Interpolate

when the median is halfway between the two values in the middle

Population Mean

μ = ∑ xi N

Standard Deviation: Equation

population: σ = √σ² sample: s = √s²

Variance: Equation

population: σ² = ∑(xi-μ)² N _ sample: s² = ∑(xi-x)² n-1

Q1, Q2, Q3, Q4: Finding Q1

(N+1)/4

Comparison of Measures: Usefulness

-mean uses all the information, but is affected by extremes -mean and median are unique, but not the mode -mode is usually less useful, but the mean and median may not actually exist in the data set

Variance: Definition

-the average of the squared deviations from the mean -includes all data values

Measures of Dispersion

1) range 2) midrange 3) quantiles 4) interquartile range 5) quartile deviation 6) variance 7) standard deviation

Sample Mean

_ x = ∑ xi n

Residual

_ xi-x

Weighted Mean

_ μw or xw = ∑ wixi ∑ wi

xi

a particular data value (for i)

Midrange

average of the lowest and highest values

Quantiles

divides the data into parts (ex percentiles, deciles, quartiles)

Skewness

either positive (tails off to the right) or negative (tails of to the left)

Quartile Deviation

half the interquartile range (Q3-Q1)/2

Symmetrical Distributions

have the left and right sides that are mirror images

Bimodal

if there are two modes

Positively Skewed if:

mean > median > mode

Measures of Central Tendency

mean, median, mode

Negatively Skewed if:

mode > median > mean

Effect of Extreme Values on Median

no effect (good and bad)