Descriptive Research Central Tendency and Variability

Presented byNor Laili Fatmawati

AminullohHendra Sudarso

PASCASARJANA UNESA 2010

Descriptive Research

Definition A research design used to obtain information concerning the current status or phenomena

PurposeTo describe the current state of affairs at the time of the study.

General steps in conducting descriptive studies

1. Stating the problem.2. Identifying the information needed to solve the problem.3. Selecting or developing the instrument for collecting data.4. Identifying the target population and determination of any necessary sampling procedure.5. Designing the procedure for data collection.6. Collecting the data.7. Analyzing the data.8. Preparing the report.

Descriptive Research

Some studies that can be classified as descriptive research

survey case study developmental studies follow-up studies documentary analysis trend analysis correlation studies.

Descriptive Research

Descriptive Research Survey researchSurvey research is used to study directly the characteristic of populations through the use of surveys.

Advantages • It allows the researcher to get a very broad picture of whatever is being studied• It is efficient in that the data collection part of the study is finished after one contact is made with respondents and the information is collected• If it is done properly and with minimal sampling error, surveys can yield remarkably accurate results.

Weaknesses • It can be the sources of bias, whether interviewer bias or interviewee bias• Sometimes people do not respond, as in the case of a mail survey.

Descriptive Research

Case studyCase study is a method used to study an individual or an institution in a unique setting or situation in as intense and as detailed a manner as possible.

Advantages• It allows for very close examination and scrutiny and the collection of detailed data. It encourages the use of several different technique to get the necessary information ranging from personal observations to interviews of others who might know the focus of the case study. • No other way to get a richer account of what is occurring than through a case study.• It suggests directions for further study.

Descriptive Research

Case study

Weaknesses

• What the researchers see is not always what they get.• The notes the researchers record in their journal may accurately

reflect reality or what they observe, but they may not.• What case studies provide in depth, they lose in breadth• We may not even think about trying to establish any cause-and-effect

links between what we see and what we think might be responsible for the outcomes,

• The generalizability of the findings is limited.

Descriptive Research

Developmental ResearchDevelopmental research is a method to examine changes over time.

Two methods of Developmental research1. Longitudinal method , The same sample of subjects is studied over an extended period of time.

2. Cross-sectional method. To study subjects of various age levels at the same point in time.

Descriptive Research

Follow-up StudiesThis is almost same with the longitudinal method. It is

conducted to evaluate some programs that have been conducted.

Documentary AnalysesDocumentary analyses are studying some documents for

some purposes. It is not only content analyses but also can be sociological study and psychological variables and others.

Descriptive Research

Trend AnalysesTrend analyses are conducted to predict something that will happen in the

future. The trend it self can be known from documentary analyses or surveys repeated at intervals which than possible the researchers to find the rate and direction of changes.

Correlational studiesThese studies are focus on determining the extent of relationship existing

between variables. They are conducted to measure the variation in a variable by associating it with the variation in the other variable. These studies are classified in the descriptive studies if the purpose is to describe relationship or to generate hypotheses and as ex post facto studies if hypothesis testing is the focus.

Measures of Central Tendency

Central tendency provides a single index to represent the average value of a whole set of measures.

Three kinds of central tendency Mode Median Mean.

Measures of Central Tendency

ModeDefinition The most frequently value occurs.

Example (for single data)7 7 7 7 7 8 8 9 9 9The mode is 7

Measures of Central TendencyModeExample (for data in group)

The high of Students of Pascasarjana Unesa 2010

NO. Tall Frequency

1. 140 – 149 6

2. 150 – 159 22

3. 160 – 169 39

4. 170 – 179 25

5. 180 – 189 7

6. 190 – 199 1

Total students frequency 100

98,1640

10.1417

175,159

.

Md

Mdo

Iba

aLbMdo

98,164

10.1417

145,169

.

Mdo

Mdo

Iba

bLaMdo

Measures of Central Tendency

Mode

Mdo = Modus

Lb = The limit of the lower class modus

La = The limit of the higher class modus

a =interval frequency between the nearest lower class modus or the

frequency before it.

b =interval frequency between the nearest higher class modus or the

frequency after it.

I = Class interval

Measures of Central Tendency

Median Definition The middle score in a distribution.

Example (for single data)8 7 9 7 8 6 7 9 5

5 6 7 7 7 8 8 9 9The median is 7

6 7 7 7 7 8 8 9 9 9The median is (7+8)/2 = 7,5

Measures of Central Tendency

Median Example (for data in group)The high of Students of Pascasarjana Unesa 2010

NO. Tall Frequency

1. 140 – 149 6

2. 150 – 159 22

3. 160 – 169 39

4. 170 – 179 25

5. 180 – 189 7

6. 190 – 199 1

Total students frequency 100

14,165

10.39

282

100

5,159

.2

Mdi

Mdi

Ifd

FaN

LbMdi

14,165

10.39

332

100

5,169

.2

Mdi

Mdi

Ifd

FbN

LaMdi

Measures of Central Tendency

Median Mdi = : Median

Lb = : batas bawah kelas median

La = : batas atas kelas median

N = : total frekuensi / banyaknya angka pada data

Fa = : frekuensi komulatif sebelum frekuensi kelas median atau kelas lebih rendah

Fb = : frekuensi komulatif sesudah frekuensi kelas median atau kelas lebih tinggi

fd = : frekuensi pada kelas median

I = : lebar interval

Measures of Central Tendency

Mean Definition The sum of the whole scores divided by the number of the scores.

Formula (for single data)

N

XX

X = the mean∑ = the sum ofX = raw scoreN = the number of cases

Measures of Central Tendency

Mean Example (for single data)8 7 9 7 8 6 7 9 5

N

XX

Mean = 7,33

33,79

66

Measures of Central Tendency

Mean Formula (for data in group)The age of students of Pascasarjana Unesa 2010

X

NO Age Frequency (fi) Xi fi.Xi

1. 21 – 25 6 23 138

2. 26 – 30 22 28 616

3. 31 – 35 39 33 1287

4. 36 – 40 25 38 950

5. 41 – 45 7 43 301

6. 46 – 50 1 48 48

JUMLAH 100 3340

4,33

1003340

.1

N

XifX

Mean = 33,4

Measures of Variability

X

Measure of variability tells us how spread out a group of scores are. The functions of the measure of variability: To know weather or not the mean is representative. For example:

The mean of teachers’ salary = Rp. 120.000,00Of course this mean is not representative because there are 4 teachers who have

salary under the mean. It is because the data is very heterogeneous. It helps the researcher in using statistic measurement in testing the hypothesis.

Weather or not the sample comes fromk the same population.

Teacher Salary (Rp)

A 40000

B 50000

C 55000

D 65000

E 390000

Total 600000

Measures of Variability

X

Four kinds of Measure of variability Range Quartile deviation Variance Standard deviation.

Measures of VariabilityRangeThe range gives the distance between the highest and the lowest values in a

distribution.

Formula

R = the range= the highest value in a distribution= the lowest value in distribution.

Example2 4 6 7 8 9

So, R= 9 – 2 R= 7

hX

lh XXR

lX

Measures of Variability

Quartile DeviationQuartile Deviation (QD) gives the half-distance between the upper (Q3) and lower

quartiles (Q1).

FormulaQ3 = L +

fw

cfbN

4

3

i

And for Q1, the formula is: Q1= L +

fw

cfbN

4

i

After finding Q3 and Q1, we can find the QD by the following formula: QD= 2

Q 13 Q

Q3 = the upper quartileQ1 = the lower quartileN = the number of case in the distribution

Measures of Variability

Quartile Deviation

i i

After finding Q3 and Q1, we can find the QD by the following formula:

QD= 2

Q 13 Q

Q3 = the upper quartileQ1 = the lower quartileN = the number of case in the distributionL = the lower limit of the interval within whish the quartile liescbl = the cumulative frequency below the interval containing the quartilefw = the frequency of cases within the interval containing the quartilei = the interval scale.

Measures of Variability

Variance Variance is the mean of the squared deviation scores.

Formula

σ2= N

r 2

σ2 =the variance∑ = the sum ofr = the deviation of each score from the mean (X- X ) otherwise known as the deviation score.N = the number of case in the distribution.

Measures of Variability

Standard DeviationStandard Deviation is the square root of the mean of the squared deviation

of values from the mean.

Formulaσ =

NN

XX

22

)(

σ =the standard deviation∑X2 = the sum of the squares of each score (that is, each score is first squared, then these squares are summed)(∑X2) = the sum of the scores squared (the scores are first summed, then this total is squared)N = the number of case in the distribution.

VARIANS

Year X X – (X – )2

1994 7,5 4,2 17,64

1995 8,2 4,9 24,01

1996 7,8 4,5 20,25

1997 4,9 1,6 2,56

1998 -13,7 -17,0 289,00

1999 4,8 1,5 2,25

2000 3,5 0,2 0,04

2001 3,2 -0,1 0,01

Mean

2 = (X – )2/N

26,4

3,32

355,76

44,47Total