S519: Evaluation of Information Systems

Social Statistics

Ch3: Difference

This week

Range Standard deviation Variance Using Excel to calculate them

The whole story

Descriptive statistics Centrality tendency (average) Measurement of variability (variability)

Average+Variability = describe the characteristics of a set of data

Measures of variability

Variability How scores differ from one another

Three sets of data 7, 6, 3, 3, 1 3, 4, 4, 5, 4 4, 4, 4, 4, 4

Variability = the difference from the mean

Measures of variability

Three ways Range Standard deviation Variance

Range

The most general measure of variability How far apart scores are from one another

Range = highest score – lowest score

What is the range for

98, 86, 77, 56, 48

Standard deviation

Standard deviation (SD) Average deviation from the mean (average

distance from the mean) Represents the average amount of variability

1

)( 2

n

xxs

Exercise

Calculate standard deviation

5, 8, 5, 4, 6, 7, 8, 8, 3, 6

By hand Using excel (STDEV())

STDEV and STDEVP

STDEV is standard deviation for sample (biased SD)

STDEVP is standard deviation for population (unbiased SD)

If your dataset is the whole population, use STDEVP to calculate standard deviation

If you dataset is the sample of something, use STDEV to calculate standard deviation

STDEV and STDEVP

1

)( 2

n

xxs

n

xxs

2)(

STDEV

STDEVP

Why n or n-1?

To be conservative STDEV

This is the standard deviation for sample Take n-1 in order to make STDEV a bit larger

than it would be. If we have err, we compensate by overestimating

the STDEV

Why n or n-1?

Sample size Numerator in standard deviation formula

Denominator Population standard deviationSTDEVP(dividing by n)

Denominator Sample standard deviationSTDEV(dividing by n-1)

Difference between STDEVP and STDEV

10 500 7.07 7.45 0.38

100 500 2.24 2.25 0.01

1000 500 0.7071 0.7075 0.0004

What to remember

Standard Deviation (SD) = the average distance from the mean

The larger SD, the more different data are from one another

Since mean is sensitive to extreme scores, so do SD

If SD=0, this means that there is no variability in the set of scores (they are all identical in value) – this happens very rarely.

Variance

Variance = (Standard Deviation)^2

1

)( 22

n

xxs

Exercise

Calculate variance in Excel 8, 8, 8, 7, 6, 6, 5, 5, 4, 3

Var() STDEV Varp() STDEVP

SD vs. variance

Often appears in the “Results” sections of journals

They are quite different Variance is squared SD

SD vs. variance

mean

SD = 1.76Variance = 3.1

Average distance to mean=(2+2+2+1+1+1+2+3)/10=1.4

Exercise 1 (S-p78-problem2)

Calculate range, STDEV and STDEVP and variance by hand or calculator 31, 42, 35, 55, 54, 34, 25, 44, 35

Use Excel to do that.

Exercise 2 (S-p79-problem4)

Problem 4 in S-p79 Calculate the

variation measures for height and weight

Height Weight53 15646 13154 12344 14256 15676 17187 14365 13545 13844 11457 15468 16665 15366 14054 14366 15651 17358 14349 16148 131

Exercise 3 (S-p79-problem5)

Western Airlines Flight Report Thursday Friday Thursday Friday Thursday FridayMorning Flights To Kansas To Kansas To Philadelphia To Philadelphia To Providence To ProvidenceNumber of passengers 258 251 303 312 166 176 Thursday Friday Thursday Friday Thursday FridayEvening Flights To Kansas To Kansas To Philadelphia To Philadelphia To Providence To ProvidenceNumber of passengers 312 331 321 331 210 274

Exercise 3 (S-p79-problem5)

Look at problem 5 Write a half page summary report to your

boss Form a group to discuss it