PSY201: Chapter 4 - Variability

Question 1

Variability

Answer 1

distribution only partially described through a measure of central tendency
describe distributions in terms of central tendency + variability

Question 2

Variability

Answer 2

describe how much scores differ from that average

Question 3

Variability

Answer 3

to obtain a measure of how spread out the scores are in a distribution
usually accompanies measure of central tendency as basic descriptive statistics for a set of scores

Question 4

Central Tendency

Answer 4

describes central point of the distribution

variability describes how scores are scattered around that central point

Question 5

Central Tendency and Variability

Answer 5

2 primary values used to describe distribution of scores

Question 6

Variability

Answer 6

distributions differ from each other in terms of how much scores deviating from mean

Question 7

Variability

Answer 7

shows how well an individual score represents the entire
distribution
how much error to expect - important for making conclusions from small samples using inferential statistics.

Question 8

Variability

Answer 8

both descriptive measure + important component of most inferential statistics
descriptive statistic - measures degree to which scores are spread out/clustered together in a distribution

Question 9

Variability

Answer 9

inferential statistics - measure of how accurately any individual score/sample represents the entire population.

Question 10

Variability

Answer 10

pop variability small ⇒ scores clustered close together + individual score/sample will provide good representation of entire set
variability large ⇒ scores widely spread, easy for 1/2 extreme scores to give distorted picture of general pop

Question 11

Measuring Variability

Answer 11

Range: Diff betw highest + lowest score
Interquartile range: Point of the 25th percentile + point of 75th percentile.
Standard Deviation/Variance: Avg squared distance from mean - most important variability measure
variability determined by measuring distance

Question 12

Range

Answer 12

distance from largest-smallest score in distribution

defined in terms of distance - interval/ratio scale measurements of continuous variable

Question 13

Range

Answer 13

take diff betw upper real limit of largest X + lower real limit of smallest X value
Range= URLXmax–LRLXmin

Question 14

Range

Answer 14

simple way to describe spread of scores
completely dependent on max + min scores
Outliers can have huge influence on this measure of dispersion
range considered to be least important measure of variability

Question 15

Interquartile Range

Answer 15

avoid being influenced by extreme, potentially unrepresentative, scores
distance covered by middle 50% of distribution
25th, 50th + 75th %iles are quartiles” because they cut the sample into four equal parts.
= Q3 – Q1

Question 16

Interquartile Range

Answer 16

figure out how many scores represent 1⁄4 of the data
refer to range of middle 2 quarters
Interquartile range = Q3 - Q1

Question 17

Interquartile Range

Answer 17

semi-interquartile range: half of the interquartile range

measures distance from middle of the distribution to boundaries that define the middle 50% = (Q3−Q1)/2

Question 18

Interquartile Range

Answer 18

more stable than the range - not influenced by outliers
disadvantage - using 50% of scores leaves out much of data doesn’t give complete pic of variability
considered to be a crude reduction of the data

Question 19

Standard Deviation and Variance for a Population

Answer 19

better measure - considers distance of each score

want to measure standard/typical distance from the mean

Question 20

Standard Deviation and Variance for a Population

Answer 20

Deviation score = X − μ

Question 21

Standard Deviation and Variance for a Population

Answer 21

sign - direction of value from mean (above/below)

Question 22

Standard Deviation and Variance for a Population

Answer 22

Because deviation scores built about mean - must sum to zero

Sum of deviations = Σ(X - μ)

Question 23

Standard Deviation and Variance for a Population

Answer 23

avg deviation of scores around mean always zero

meaningless measure for variability

Question 24

Standard Deviation and Variance for a Population

Answer 24

Square diff (deviation) before calculating sum of deviations, - sum of squares
take into account magnitude but not direction of the difference from the means

Question 25

Population variance

Answer 25

mean of the squared deviations | avg of squared distances from the mean (sum of squares)

Question 26

Standard Deviation

Answer 26

we correct for squaring the means by taking the square root of variance =√variance

Question 27

Standard Deviation

Answer 27

square root of the avg squared deviation | avg distancefromthemean.

Question 28

Standard Deviation

Answer 28

we cannot compute for nominal/ordinal scales

Question 29

sum of squared deviations

Answer 29

SS=∑(X−μ)2 Find each deviation score Square each deviation score + Add squared deviations

Question 30

Variance

Answer 30

σ^2 = SS/N | mean squared deviation

Question 31

Standard Deviation

Answer 31

σ = square root of mean squared deviations √SS/N estimate of average deviation σ = √∑(X−μ)2/N

Question 32

Sample Variance and Standard Deviation

Answer 32

need to estimate population parameters from sample samples statistics give biased estimations of pop parameters underestimate pop variance

Question 33

Sample Variance and Standard Deviation

Answer 33

∑(X−M)2 Computational Formula: SS= ∑(X)^2-(∑X)2/n s^2 = ∑(X−M)2/n-1 s=√∑(X−M)2/n-1

Question 34

Summary of Computing Standard Deviations

Answer 34

Compute deviation (distance from the mean) for each score. Square each deviation. Compute mean of the squared deviations. sum the squared deviations (SS) + divide by N

Question 35

Summary of Computing Standard Deviations

Answer 35

divide the sum of the squared deviations (SS) by n - 1, rather than N. n - 1 - df: sample variance will provide an unbiased estimate of the pop variance square root of variance to obtain the standard deviation.

Question 36

Degrees of freedom (df) and bias

Answer 36

represents # scores in sample independent + free to vary | We estimate pop mean with sample mean, M.

Question 37

Sample Variance and Standard Deviation

Answer 37

apply corrections to formulas using sample data ⇒ unbiased estimates of pop variance ag of all possible sample variances pop will produce accurate estimate of pop variance

Question 38

More About Variance and Standard | Deviation

Answer 38

68% of scores lie within one standard deviation of the mean | 95% within two standard deviations

Question 39

Transformations of Scale

Answer 39

add constant to each score - value of mean changes | each score still same distance away from mean

Question 40

Transformations of Scale

Answer 40

adding constant will move each score so entire distribution is shifted to a new location centre of the distribution (the mean) changes, but standard deviation remains the same

Question 41

Transformations of Scale

Answer 41

Multiplying by constant will multiply distance betw scores | standard deviation measure of distance so it will also be multiplied