TASK 4 Sold Price sorted in order from lowest to highest 112

TASK 4

Sold Price’ sorted in order from lowest to highest.

112

114

152

230

239.5

295

305

310

323

340

342

347

350

357

358.5

375

375

410

432.5

445

446

455

460

465

475

481

490

491

510

525

552

560

563

596

615

618

670

700

711

882.5

951

1060

1175

1225

1360

1885

2020

TASK 5

SOLD PRICE ($000)

Mean

577.7447

Standard Error

58.47

Median

465

Mode

375

Standard Deviation

400.85

Sample Variance

160677.80

Kurtosis

6.91

Skewness

1.97

Range

1908

Minimum

112

Maximum

2020

Sum

27154

Count

47

QUESTION 1

Calculate, using Standard Normal tables, approximately how many “Sold Price” data values in your sample you would expect to lie within 1.5 standard deviations of the mean (i.e. between z = –1.5 and z = +1.5).

           QUESTION 2

Use your sorted “Sold Price” sample data from Task 4, and the mean and standard deviation from the Descriptive Statistics table of Task 5, to manually count the number of “Sold Price” data values in your sample that lie within 1.5 standard deviations of the mean. And State whether this count matches, approximately, your answer to question 1

112	114	152	230	239.5	295	305	310	323	340
342	347	350	357	358.5	375	375	410	432.5	445
446	455	460	465	475	481	490	491	510	525
552	560	563	596	615	618	670	700	711	882.5
951	1060	1175	1225	1360	1885	2020

Solution

1.

Using normal tables/technology, the left tailed areas of z = 1.5 and z = -1.5 are

P(z<-1.5) = 0.066807201
P(z<1.5) = 0.933192799

Thus, the area between these two z scores is

P(-1.5<z<1.5) = 0.866385597 [answer]

Thus, there are approximately 0.866385597*47 = 40.72012308

or 41 items within 1.5 standard deviations.

*******************

2.

Here,

Mean = 577.7447
Standard deviation = 400.85

Thus,

Lower bound = Mean - 1.5*standard deviation = -23.5303
Upper bound = Mean + 1.5*standard deviation = 1179.0197

There are 43 items out of 47 that lie between these two numbers. [answer]

This is quite close to the result in Part 1.