Real Estate Data Analysis and Interpretation

This assignment involves analyzing a dataset of real estate properties. Students calculate descriptive statistics like mean, standard deviation, and range for 'Sold Price' and 'Building Type'. They then construct 90% and 95% confidence intervals for the mean 'Sold Price' and the proportion of Brick Veneer buildings. The analysis assesses the reliability of these estimates and explores the impact of confidence level on interval width.

Running head: BUSINESS STATISTICS
Business Statistics
Name of the student
Name of the university
Author’s note

1BUSINESS STATISTICS
Table of Contents
Assignment I....................................................................................................................................3
TASK 1............................................................................................................................................3
Part a............................................................................................................................................3
Part b............................................................................................................................................4
Assignment II...................................................................................................................................6
TASK 2............................................................................................................................................6
Part a............................................................................................................................................6
Part b............................................................................................................................................6
Part c............................................................................................................................................7
TASK 3............................................................................................................................................7
Part a............................................................................................................................................7
Part b............................................................................................................................................8
Part i.........................................................................................................................................8
Part ii........................................................................................................................................8
Part c............................................................................................................................................8
Part d............................................................................................................................................8
TASK 4............................................................................................................................................8
Part a............................................................................................................................................8
Part b............................................................................................................................................9
Part c............................................................................................................................................9
Part i.........................................................................................................................................9
Part ii........................................................................................................................................9
TASK 5..........................................................................................................................................10
Part a..............................................................................................................................................10
Part b..........................................................................................................................................10
Part c..........................................................................................................................................10
TASK 6..........................................................................................................................................11
Part a..........................................................................................................................................11

2BUSINESS STATISTICS
Part i.......................................................................................................................................11
Part ii......................................................................................................................................11
Part iii.....................................................................................................................................11
Part b..........................................................................................................................................12
TASK 7..........................................................................................................................................12
Part a..........................................................................................................................................12
Part i.......................................................................................................................................12
Part ii......................................................................................................................................12
Part b..........................................................................................................................................13
Part c..........................................................................................................................................13

3BUSINESS STATISTICS
Assignment I
TASK 1
Part a
My student ID is 45759(801). Thus, according to the problem I would have to select the
1st row and the 8th Column. The number at 1st row and 8th column is 628952. Since the first and
last three digits both are above 400 hence the next suitable number is 115. The first 50 numbers
from 001 to 400 have been striked. Repeated numbers between 001 and 400 are highlighted.

4BUSINESS STATISTICS
Part b
My sample of population property data
Sl. No. PN V1 V2 V3 V4 V5 V6 V7 V8
1 115 3 1 2 2 5 613 450
2 150 3 1 1 1 5 412 1126 989
3 331 4 1 1 3 4 122 882.5 819
4 335 1 1 3 2 7 805 461.25 391
5 166 1 1 4 1 5 697 400 330
6 140 1 1 1 1 8 1092 1885 1755
7 162 2 0 3 2 4 385 320
8 304 1 0 2 2 4 440
9 3 1 0 1 2 4 453 389
10 197 2 3 4 600 125 97
11 170 1 1 3 3 5 589 525 455
12 385 3 1 3 2 8 655 1215 1029
13 49 3 1 1 3 7 875 1606 1474
14 309 4 0 1 1 2 354 279
15 386 3 1 1 2 5 737 610 548
16 214 3 1 3 1 5 1241 1225 1060
17 138 1 0 1 2 5 670 614
18 369 2 1 4 3 5 580 375 313
19 80 1 1 1 1 6 985 1175 1034
20 381 2 1 3 2 6 672 400 332
21 13 3 0 3 2 3 475 425
22 347 4 0 1 1 3 323 266
23 344 2 1 3 2 4 300 295 284
24 290 1 1 1 3 3 239 446 391
25 198 2 3 4 560 112 87
26 167 1 0 3 2 3 357 305
27 9 2 1 1 1 6 604 350 279
28 234 2 1 4 3 5 350 410 359
29 121 3 0 1 2 3 342 289
30 103 1 1 1 2 6 500 460 399
31 104 1 1 3 2 5 600 455 383
32 79 1 1 1 2 5 288 340 266
33 248 1 1 1 1 7 500 2020 1896
34 334 1 1 3 2 7 634 481 428
35 10 2 0 1 1 2 239.5 221
36 395 3 1 2 3 8 527 720
37 146 4 1 1 3 3 248 615 554
38 192 2 3 4 496 114 98

5BUSINESS STATISTICS
39 286 3 0 1 2 5 1060 921
40 209 3 1 1 1 5 603 951 753
41 15 2 1 1 3 5 585 563 491
42 394 3 0 1 1 4 1200 1063
43 356 3 1 4 1 3 132 618 548
44 227 3 0 3 2 5 490 440
45 371 2 3 4 1160 265 238
46 362 1 1 3 2 6 630 305 255
47 281 4 1 1 3 3 115 711 654
48 86 3 1 4 3 4 732 347 288
49 240 3 1 1 2 5 890 525 457
50 119 3 0 3 1 2 310 239

6BUSINESS STATISTICS
Assignment II
TASK 2
Part a
Table 1: Frequency Distribution of Building Types
Bld. Type Frequency
Br 14
BrV 21
Wbrd 11
VL 4
Br BrV Wbrd VL
0
5
10
15
20
25
Frequency Column Chart of
Building Type
Building Type
Frequency
Figure 1: Frequency Distribution of Building Types
For my selected sample there are 14 Brick Buildings.
Part b
For my selected sample the frequency count of Brick Veneer Buildings is the highest.

7BUSINESS STATISTICS
Part c
Br
28%
BrV
42%
Wbrd
22%
VL
8%
Relative Frequency Pie Chart for Buidling
Type
Figure 2: Relative Frequency Distribution of Building Types
The proportion of weatherboard buildings is 22% for the sample data.
TASK 3
Part a
Table 2: The Sold Prices of the Houses
Sold Prices (V7)
112 340 400 490 882.5
114 342 410 525 951
125 347 446 525 1060
239.5 350 453 563 1126
265 354 455 610 1175
295 357 460 615 1200
305 375 461.25 618 1215
310 385 475 670 1225
323 400 481 711 1606
1885
2020

8BUSINESS STATISTICS
Part b
Part i
The location of the 70th percentile is Lp= ( n+1 )∗P
100
Here “n” = 50
And “P” = 70
Thus 70th percentile = ( 50+1 )∗70
100 =35.7 ≈ 36
Hence, the 70th percentile is $711 (000s)
Part ii
The location of the 1st quartile is Q1= ( 50+1 )∗25
100 =12.75≈ 13
Hence, the 1st Quartile = $350 (000s)
The location of the 3rd quartile is Q3= ( 50+1 )∗75
100 =38.25 ≈38
Hence, the 3rd Quartile = $951 (000s)
Part c
The 70th percentile value of the sold prices is $711 (000s). Hence, we can infer that 70%
of the houses have a sold price less than or equal to $711 (000s).
Part d
IQR=Q3 −Q1=951−350=601
The IQR provides information that the range of the middle 50% of the houses was $601
(000s) between $951 and $350 (000s).
TASK 4
Part a
Descriptive Statistics for sold Prices in 000s.

9BUSINESS STATISTICS
Sold prices (000s)
Mean 618.133
Standard Error 64.048
Median 460
Mode 400
Standard Deviation 439.089
Sample Variance 192799.114
Kurtosis 2.32
Skewness 1.62
Range 1908
Minimum 112
Maximum 2020
Sum 29052.3
Count 47
Part b
IFUL=Q3 +1.5∗IQR
¿ 951+1.5∗601≈ 1853
IFLL=Q1−1.5∗IQR
¿ 350−1.5∗601=−551
Part c
Part i
Based on calculations in “part b” the central tendency measure is median. IQR depends
on 1st and 3rd Quartile. Median is 2nd Quartile.
Part ii
Based on calculations in “part b” the measure of dispersion would be IQR. It is the
difference between 3rd and 1st Quartile. It also provides information of the spread of the middle
50% of the sold prices.

10BUSINESS STATISTICS
TASK 5
Part a
Sold prices (000s)
Mean 618.133
Standard Error 64.048
Median 460
Mode 400
Standard Deviation 439.089
Sample Variance 192799.114
Kurtosis 2.32
Skewness 1.62
Range 1908
Minimum 112
Maximum 2020
Sum 29052.3
Count 47
Three prices of information which provides information regarding the distribution of the
data are Mean, median and Skewness. When Mean > Median then data is skewed right. In the
sample data the mean ($618.133) is more than the median ($460). Hence the data is skewed
right.
This is confirmed by skewness of the data (1.62). Data is positively skewed.
Part b
From the standard normal table
P ( z←1.5 )=0.0668
P ( z>1.5 )=0.9332
Hence, P (−1.5< z <1.5 )=0.9332−0.0668=0.8664 ≈ 0.87
Hence, 87% of the samples would fall within ±1.5 standard deviations
Part c
The mean sold price = $618.133 (000s)
The standard deviation of the sold price = $439.089 (000s)
Hence, upper bound = 618.133+1.5∗439.089 ≈ 1277

11BUSINESS STATISTICS
The lower bound = 618.133−1.5∗439.089≈−41
44 houses have a price less than $1277 (000s). thus 88% of the houses lie within the
upper and lower bounds. Hence, data is normally distributed.
TASK 6
Part a
Part i
Sold Prices ($000s)
Mean 618.133
Standard Error 64.048
Median 460
Mode 400
Standard Deviation 439.089
Sample Variance 192799.114
Kurtosis 2.323
Skewness 1.617
Range 1908
Minimum 112
Maximum 2020
Sum 29052.250
Count 47
Confidence Level(90.0%) 107.514
The point estimate of the Sold Prices is $613.133 (000s)
Part ii
The 90% confidence interval estimate of the mean “Sold Price”
618.133−e ≤ μ ≤ 618.133+e
618.133−107.514 ≤ μ ≤ 618.133+107.514
510.619 ≤ μ ≤ 725.647 ($000s)
Part iii
The above calculations show’s that there is a 90% chance that when another sample of 50
houses is taken, the mean sold prices of the houses would be within $510.619 and $725.647
(000s).

12BUSINESS STATISTICS
Part b
The above 90% confidence interval is satisfactory due to the fact that $650 (000s) lies
within the lower and upper bounds.
TASK 7
Part a
Building Type
Mean 0.42
Standard Error 0.071
Median 0
Mode 0
Standard Deviation 0.499
Sample Variance 0.249
Kurtosis -1.969
Skewness 0.334
Range 1
Minimum 0
Maximum 1
Sum 21
Count 50
Confidence Level(99.0%) 0.189
The proportion of Brick Veneer Buildings in the sample is 42%
Part i
The point estimate for the proportion of Brick Veneer Buildings = 0.42
Part ii
0.42−e ≤ μ ≤ 0.42+e
0.42−0.189≤ μ ≤ 0.42+0.189
0.231 ≤ μ ≤ 0.609
The lower and upper bounds, 99% confidence interval for the proportion of Brick Veneer
Buildings is 0.231 and 0.609

13BUSINESS STATISTICS
Part b
0.42−z∗se ≤ μ ≤ 0.42+z∗se
0.42−1.96∗0.071 ≤ μ ≤ 0.42+1.96∗0.071
0.42−0.139≤ μ ≤ 0.42+0.139
0.281 ≤ μ ≤ 0.559
The lower and upper bounds of 95% confidence interval for the proportion of Brick
Veneer buildings is 0.281 and 0.559 respectively.
Part c
The above calculations show that the bounds of 99% confidence interval are wider than
95% confidence interval. Hence, the lesser the confidence interval the higher the precision.
From the above calculations it can be inferred that confidence interval affects the
precision.