Social statistics Descriptive statistics Inferential statistics Mean, median and mode Z519--Spring 2015.

Social Statistics: Difference

Social statistics Descriptive statistics Inferential statistics Mean, median and mode

Review

Z519--Spring 2015

Range Variance Standard deviation Using Excel and SPSS to calculate

them

Outline

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

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

The whole story

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 Variance Standard deviation

Measures of variability

The most general measure of variability

How far apart scores are from one another

Range

Range = highest score – lowest score

What is the range for the follow numbers? 98, 86, 77, 56, 48

Variance The average of the squared deviations

from the mean

Variance

1

)( 22

n

xxs

Standard deviation (SD) Average deviation from the mean

(average distance from the mean) Represents the average amount of

variability

Standard deviation

1

)( 2

n

xxs

: the deviation from the mean : the sum of the squared deviations

from the mean : the number of scores : the variance : the standard deviation

Variance and SD

The right figure shows 2013 GDP per Capita for select countries--current US$

Please calculate the variance and standard deviation by hand or by using excel (VAR.S() & STDEV.S())

Exercise

Data collected from http://data.worldbank.org/

CountryGDP per Capita

Afghanistan 678Brazil 11208Canada 51958Chile 15732Greece 21910Japan 38492Lebanon 9928Norway 100819Panama 11037Saudi Arabia 25852Singapore 55182Tunisia 4329United States 53143Vietnam 1911Zimbabwe 905

1

)( 2

n

xxs

STDEV.S and STDEV.P

n

xxs

2)(

STDEV.S

STDEV.P

𝑠2

𝑠2

VAR.S

VAR.P

STDEV.S is standard deviation for sample (biased SD)

STDEV.P is standard deviation for population (unbiased SD)

If your dataset is the whole population, use STDEV.P to calculate standard deviation

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

STDEV.S and STDEV.P

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 error, we compensate by

overestimating the STDEV

Why n or n-1?

Sample size

Numerator in standard deviation formula

Denominator Population standard deviationSTDEV.P(dividing by n)

Denominator Sample standard deviationSTDEV.S(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

Why n or n-1?

Often appears in the “Results” sections of journals

They are quite different Variance is squared SD

SD vs. Variance

SD vs. Variance

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

mean

SD = 1.76Variance = 3.1

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

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.

What to remember

Average life expectancy for females in 2010-2011 is reported for 10 countries. Please calculate the range, variance and SD for European counties, Non-European countries, and all countries.

Exercise 1

You and your friends have just measured the heights of your dogs (in millimeters):

The heights (in mm) (at the shoulders) are: 600, 470, 170, 430 and 300.

Find out the Mean, the Variance, and the Standard Deviation.

Exercise 2

Western Airlines Flight Report             

  Thursday Friday Thursday FridayThursday Friday

Morning Flights To Kansas To Kansas

To Philadelphia

To Philadelphia

To Providence

To Providence

Number of passengers 258 251 303 312 166 176             

  Thursday Friday Thursday FridayThursday Friday

Evening Flights To Kansas To Kansas

To Philadelphia

To Philadelphia

To Providence

To Providence

Number of passengers 312 331 321 331 210 274             

Exercise 3

Write a half page summary report to your boss

Form a group to discuss it

Exercise 3