Statistika Ekonomi Dan Bisnis

Agus SalimFakultas Ekonomi Universitas Indonesia

Quiz

Ganjil1. Arti Statistika?2. Data Kuantitatif?3. Sampel?

Genap1. Kegunaan Statistika?2. Data kualitatif?3. Populasi?

Kumpulkan!!!

10 minutes oral quiz (tanya jawab 10 menit)Ukuran-ukuran Sentral dan Persebaran (cont) Koefisien Variasi Perhitungan Kuartil dan PersentilEksplorasi Data Pendahuluan: Pengantar ke Eksplorasi Data Pemeriksaan Pola Data berstruktur Tunggal Diagram Dahan Daun

Silabus

Pengertian tentangPopulasi dan Sampel

A population is a collection of all possible individuals, objects, ormeasurements of interest.

A sample is a portion, or part, of the population of interest

The central tendency is the middle ortypical values of a distribution.

Central tendency can be assessed using adot plot, histogram or more precisely withnumerical statistics.

Central TendencyCentral Tendency

Statistic Formula Excel Formula Pro Con

Mean=AVERAGE(Data)

Familiar anduses all thesampleinformation.

Influenced byextremevalues.1

1 ni

ix

n

Central TendencyCentral Tendency

Six Measures of Central Tendency

Tabel 2.3

Median

Middlevalue insortedarray

=MEDIAN(Data)Robust whenextreme datavalues exist.

Ignoresextremes andcan beaffected bygaps in datavalues.

Statistic Formula Excel Formula Pro Con

Mode Mostfrequentlyoccurringdata value

=MODE(Data)

Useful forattributedata ordiscrete datawith a smallrange.

May not beunique,and is nothelpful forcontinuousdata.

Central TendencyCentral Tendency Six Measures of Central Tendency

Midrange=0.5*(MIN(Data)

+MAX(Data))

Easy tounderstandandcalculate.

Influencedby extremevalues andignoresmost datavalues.

min max

2x x

Tabel 2.3

Statistic Formula Excel Formula Pro Con

Geometricmean (G)

=GEOMEAN(Data)

Useful forgrowth ratesandmitigateshighextremes.

Lessfamiliar andrequirespositivedata.

Trimmedmean

Same as themean exceptomit highestand lowest k%of data values(e.g., 5%)

=TRIMMEAN(Data, %)

Mitigateseffects ofextremevalues.

Excludessome datavalues thatcould berelevant.

Central TendencyCentral Tendency

Six Measures of Central Tendency

1 2 ...n

nx x x

Tabel 2.3

ContohMean, Median, Modus, Mid Range, Geometric Mean,

Trimmed Mean

Tinggi badan mahasiswa Upah di perusahaan x Harga beras Jarak kampus tempat tinggal mahasiswa

(copy data mahasiswa dari siak ng)

No Nama Program Studi1 Rini Yamasari Manajemen - Ekstensi2 Ahmad Safwat Manajemen - Ekstensi3 Delasya Mutiara Manajemen - Ekstensi4 George Michael Chuck Norris Manajemen - Ekstensi5 H P Likel Wandy Gultom Manajemen - Ekstensi6 Ira Juliana Siagian Manajemen - Ekstensi7 Raynard Daniel Finantar Manajemen - Ekstensi8 Rizka Estisia Pratiwi Manajemen - Ekstensi9 Rizki Kumoro Setiadi Manajemen - Ekstensi

10 Sawitri Manajemen - Ekstensi11 Yulia Rahmadini Manajemen - Ekstensi12 Alyssa Noviera Dwiharti Akuntansi - Ekstensi13 Bagus Kurniawan Akuntansi - Ekstensi14 Edwina Pinka Anggarani Akuntansi - Ekstensi15 Elfira Akuntansi - Ekstensi16 Isabella Mulyawati Akuntansi - Ekstensi17 Ken Anissa Akuntansi - Ekstensi18 Marcellina Cynthia Cindy Lupita Akuntansi - Ekstensi19 Mohamad Nurreza Rachman Akuntansi - Ekstensi20 Novrizal Nugroho Akuntansi - Ekstensi21 Pricelia Puteri Ramadhani Akuntansi - Ekstensi22 Shella Keshia Prameswari Akuntansi - Ekstensi

Dispersion

Why Study Dispersion? A measure of location, such as the mean or the

median, only describes the center of the data. It isvaluable from that standpoint, but it does not tell usanything about the spread of the data.

For example, if your nature guide told you that theriver ahead averaged 3 feet in depth, would you wantto wade across on foot without additional information?Probably not. You would want to know somethingabout the variation in the depth.

A second reason for studying the dispersion in a setof data is to compare the spread in two or moredistributions.

Samples of Dispersions

Measures of Dispersion

Range

Mean Deviation

Variance and StandardDeviation

EXAMPLE RangeThe number of cappuccinos sold at the Starbucks location in the Orange

Country Airport between 4 and 7 p.m. for a sample of 5 days last yearwere 20, 40, 50, 60, and 80. Determine the Range and mean deviationfor the number of cappuccinos sold.

Range = Largest Smallest value= 80 20 = 60

EXAMPLE Variance and StandardDeviation

The number of traffic citations issued during the last fivemonths in Beaufort County, South Carolina, is 38, 26, 13,41, and 22. What is the population variance?

EXAMPLE Sample VarianceThe hourly wages for a sample of part-time employees at Home Depot

are: $12, $20, $16, $18, and $19. What is the sample variance?

The Empirical Rule

The Arithmetic Mean of GroupedData

ADA PR UNTUK RINGKASANSLIDE DIBAWAH

130227

Recall in Chapter 2,we constructed afrequencydistribution for thevehicle sellingprices. Theinformation isrepeated below.Determine thearithmetic meanvehicle selling price.

The Arithmetic Mean of Grouped Data -Example

The Arithmetic Mean of GroupedData - Example

Standard Deviation of GroupedData

Standard Deviation of GroupedData - Example

Refer to the frequency distribution for the Whitner Autoplexdata used earlier. Compute the standard deviation of thevehicle selling prices

Stem-and-Leaf In Chapter 2, we showed how to organize data into a frequency

distribution. The major advantage to organizing the data into afrequency distribution is that we get a quick visual picture of theshape of the distribution.

One technique that is used to display quantitative information in acondensed form is the stem-and-leaf display.

Stem-and-leaf display is a statistical technique to present a set ofdata. Each numerical value is divided into two parts. The leadingdigit(s) becomes the stem and the trailing digit the leaf. The stemsare located along the vertical axis, and the leaf values are stackedagainst each other along the horizontal axis.

Advantage of the stem-and-leaf display over a frequency distribution- the identity of each observation is not lost.

Stem-and-leaf: Another ExampleListed in Table 41 is the number of 30-second radio advertising spots purchased by

each of the 45 members of the Greater Buffalo Automobile Dealers Associationlast year. Organize the data into a stem-and-leaf display. Around what values dothe number of advertising spots tend to cluster? What is the fewest number ofspots purchased by a dealer? The largest number purchased?

Spots cumulative lower upper midpoint width frequency percent frequency percent

80 < 90 85 10 2 4.4 2 4.490 < 100 95 10 7 15.6 9 20.0

100 < 110 105 10 6 13.3 15 33.3110 < 120 115 10 9 20.0 24 53.3120 < 130 125 10 8 17.8 32 71.1130 < 140 135 10 7 15.6 39 86.7140 < 150 145 10 3 6.7 42 93.3150 < 160 155 10 3 6.7 45 100.0

45 100.0

Spots cumulative lower upper midpoint width frequency percent frequency percent

80 < 90 85 10 2 4.4 2 4.490 < 100 95 10 7 15.6 9 20.0

100 < 110 105 10 6 13.3 15 33.3110 < 120 115 10 9 20.0 24 53.3120 < 130 125 10 8 17.8 32 71.1130 < 140 135 10 7 15.6 39 86.7140 < 150 145 10 3 6.7 42 93.3150 < 160 155 10 3 6.7 45 100.0

45 100.0

Stem-and-Leaf Example

Suppose the seven observations inthe 90 up to 100 class are: 96, 94,93, 94, 95, 96, and 97.

The stem value is the leading digit ordigits, in this case 9. The leavesare the trailing digits. The stem isplaced to the left of a vertical lineand the leaf values to the right.The values in the 90 up to 100class would appear as

Then, we sort the values within eachstem from smallest to largest.Thus, the second row of the stem-and-leaf display would appear asfollows:

Stem-and-leaf: AnotherExample

Stem-and-leaf: Another Example(Minitab)

The standard deviation is the most widely usedmeasure of dispersion.

Alternative ways of describing spread of data includedetermining the location of values that divide a set ofobservations into equal parts.

These measures include quartiles, deciles, andpercentiles.

Quartiles, Deciles and Percentiles

To formalize the computational procedure, let Lp refer to thelocation of a desired percentile. So if we wanted to find the 33rdpercentile we would use L33 and if we wanted the median, the50th percentile, then L50.

The number of observations is n, so if we want to locate themedian, its position is at (n + 1)/2, or we could write this as(n + 1)(P/100), where P is the desired percentile.

Percentile Computation

Percentiles - ExampleListed below are the commissions earned last month by a

sample of 15 brokers at Salomon Smith BarneysOakland, California, office. Salomon Smith Barney is aninvestment company with offices located throughout theUnited States.

$2,038 $1,758 $1,721 $1,637$2,097 $2,047 $2,205 $1,787$2,287 $1,940 $2,311 $2,054$2,406 $1,471 $1,460

Locate the median, the first quartile, and the third quartilefor the commissions earned.

Percentiles Example (cont.)Step 1: Organize the data from lowest to largest value

$1,460 $1,471 $1,637 $1,721$1,758 $1,787 $1,940 $2,038$2,047 $2,054 $2,097 $2,205$2,287 $2,311 $2,406

Step 2: Compute the first and third quartiles. Locate L25 and L75using:

205,2$721,1$

lyrespectivearray,in thenobservatio12thand4th thearequartiles thirdandfirst theTherefore,

1210075)115(4

10025)115(

75

25

7525

LL

LL

Percentiles Example (Minitab)

Percentiles Example (Excel)