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Measures of Dispersion

April 27, 2020

Measuresof Dispersion

Whereasmean, mode, and median are measures of central tendency, there arealso measures of dispersion or spread in statistics, referred to asvariability of scatter. Measures of dispersion include standarddeviation, variance, interquartile range, and range. They measure thedegree to which a statistical data is either squeezed together orscattered. The most commonly used are range, interquartile range,variance, and standard deviation.

Rangeshows the difference between the highest and the lowest figure orentry. The lowest in this case is $32 while the highest is $2409.Therefore, the range is $2377.

Standarddeviation is calculated by first calculating the variance, which isobtained by

Where,X is the mean, M is the data, while n is the population

Populationmean equals total divide by the population size, which comes to: $(89992/60) = $1499.86

ThusApproximately $1500

Scomes to $ 592

Coefficientof skewness is obtained by,

WhereMd is median and S is standard deviation

=-0.52956

Thefirst quartile shows the 25thpercent value while the third quartile shows the 75thpercent value.

1srquartile=$1120

3rdquartile=$1913

Interpretationsand Conclusion

Thestandard deviation of $ 592 in the bank balances here shows that thevalues are values in the population are $592 close or far from thepopulation mean. In this case, they are not so concentrated aroundthe mean or average. The big margin in the standard deviation of bankbalances could be informed by outlies, i.e. figures that are tooextreme like $32 and $2409

Thedistribution is negatively skewed or skewed to the left. Thus thedistribution is in such a way that those balances that fall below themean are more than those that fall above the mean

Appendix

Standard deviation

Value (X)

(X-M)

(X-M)(X-M)

32

1157

1338649

137

920

846400

167

752

565504

343

610

372100

580

494

244036

Mean

1499.866667

634

456

207936

740

282

79524

748

180

32400

765

26

676

789

6

36

890

-1

1

1006

-93

8649

1044

-208

43264

1053

-284

80656

First quartile

1120

-386

148996

Variance

350357.23

1125

-413

170569

Standard deviation

591.909

1169

375

140625

Approximately

592

1218

162

26244

1266

-26

676

1320

-116

13456

1326

-175

30625

1338

-246

60516

1455

-256

65536

1474

-385

148225

Median

1604.5

1487

-458

209764

1494

-489

239121

1501

-495

245025

1526

-576

331776

1554

-625

390625

Skewsness

3(1500-1604.5)

Second quartile

1593

-656

430336

592

1616

-704

495616

1622

-875

765625

1645

-909

826281

1675

1468

2155024

1708

1363

1857769

1735

760

577600

1746

447

199809

1756

380

144400

1784

174

30276

1790

45

2025

1831

-54

2916

1838

-235

55225

1885

-290

84100

1886

-331

109561

Third quartile

1913

-338

114244

1958

-644

414736

1989

-776

602176

1995

1333

1776889

2051

866

749956

2076

735

540225

2125

711

505521

2138

331

109561

2144

234

54756

2156

13

169

2204

-122

14884

2215

-145

21025

2276

-551

303601

2375

-638

407044

2409

-715

511225

2557

-1057

1117249

89992

&nbsp

21021434

&nbsp

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