Real Estate Data Analysis and Confidence Intervals

This solved assignment focuses on analyzing real estate data. It calculates various descriptive statistics like mean, standard deviation, and median for both sold prices and the proportion of brick veneer buildings. It then constructs 90% and 99% confidence intervals for these values, demonstrating how confidence level affects interval width. The assignment also explores interpreting the confidence intervals in the context of real estate trends.

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

1BASIC BUSINESS 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............................................................................................................................................6
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............................................................................................................................................9
Part a..........................................................................................................................................10
Part b..........................................................................................................................................10
Part c..........................................................................................................................................10
TASK 6..........................................................................................................................................11
Part a..........................................................................................................................................11

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Part i.......................................................................................................................................11
Part ii......................................................................................................................................11
Part iii.....................................................................................................................................11
Part b..........................................................................................................................................11
TASK 7..........................................................................................................................................11
Part a..........................................................................................................................................11
Part i.......................................................................................................................................12
Part ii......................................................................................................................................12
Part b..........................................................................................................................................12
Part c..........................................................................................................................................12

3BASIC BUSINESS STATISTICS
Assignment I
TASK 1
Part a
The Last three digits of my roll number is 375. Hence I have to choose 75th row and 3
columns. The First cell containing the number 469454 is highlighted. The first 50 three digit
numbers between 001 and 400 are strike. All repeated numbers are highlighted.

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Part b
The final sample data is the following:
PN V1 V2 V3 V4 V5 V6 V7 V8
97 3 0 1 1 3 705 630
185 2 1 3 3 5 330 510 448
201 1 1 1 2 7 20000 1010 826
164 2 1 4 1105 152 127
48 3 0 1 1 4 450 389
352 4 0 2 1 2 425
199 3 0 1 1 3 420.5 367
374 3 1 2 2 9 766 950
220 2 1 3 3 4 236 610 541
161 2 1 4 3 4 296 633 564
306 1 0 3 2 4 415 358
365 2 1 4 3 5 405 430 357
223 3 1 4 1450 1360 1208
4 4 0 1 1 3 480 410
253 3 0 1 2 4 406 335
255 1 1 2 2 5 295 710
99 3 1 1 2 9 500 1085 930
305 1 0 4 2 4 351 279
368 2 1 1 3 5 630 426 366
364 2 1 1 3 5 450 418 363
339 4 0 1 1 4 560 488
378 2 1 4 2 6 702 450 392
222 3 1 1 2 6 730 650 590
144 2 1 1 3 6 585 552 480
359 1 1 4 1 7 725 645.55 593
325 3 0 1 2 6 605 536
34 3 1 1 1 8 687 1335 1224
301 1 1 1 2 5 446 432.5 369
143 2 1 1 1 7 636 542 486
370 2 1 4 3 6 635 450 400
367 2 1 1 3 4 604 335.5 261
361 1 1 3 2 6 830 459 397
366 2 1 1 3 5 600 358.5 307
191 2 1 1 2 7 650 270 253
398 3 1 1 2 5 596 555 486
16 3 0 1 1 5 781.5 717
184 2 1 4 1 4 200 460 407
64 3 1 3 2 6 406 348 298

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320 3 1 2 3 7 2405 930
390 1 1 3 1 5 540 350 289
379 2 1 4 2 8 650 518 445
268 1 0 1 2 4 441 381
151 3 0 1 1 3 435 381
396 1 1 1 2 6 530 420.5 361
116 3 1 1 1 5 845 1800 1681
343 2 1 1 2 6 766 439 376
158 3 3 4 20000 2650 2458
345 2 1 3 3 4 620 360 304
88 4 1 1 1 5 160 890 838
228 3 1 1 1 4 435 596 536

6BASIC BUSINESS STATISTICS
Assignment II
TASK 2
Part a
The frequency count of the Building types are:
Table 1: Frequency Distribution of Building Types
Building Type Frequency Relative Frequency
Brick 16 0.32
Brick Veneer 19 0.38
Weatherboard 12 0.24
Vacant Land 3 0.06
Total 50 1
Figure 1: Frequency Distribution of Building Types
There are 16 Brick type buildings in the selected sample.
Part b
The frequency of Brick Veneer type buildings is the most in my selected sample.

7BASIC BUSINESS STATISTICS
Part c
Figure 2: Relative Frequency Distribution of Building Types
The proportion of weatherboard buildings in the selected sample is 24%.
TASK 3
Part a
Table 2: The Sold Prices of the Houses
Sold Prices (V7)
152 435 596
270 439 605
335.5 441 610
348 450 633
350 450 645.55
351 450 650
358.5 459 705
360 460 781.5
406 480 890
415 510 1010
418 518 1085
420.5 542 1335
420.5 552 1360
426 555 1800
430 560 2650
432.5

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Part b
Part i
The 70th percentile is calculated as Lp= ( n+1 ) ∗P
100
The number of samples takes “n” = 50
The percentile required “P” = 70
Hence 70th percentile = ( 50+1 )∗70
100 =35.7 ≈ 36
The value of the 36th number = 645.55 ($000s)
Part ii
The 1st quartile is calculated as L25=Q1= ( 50+1 )∗25
100 =12.75≈ 13
The value of the 13th number = 420.5 ($000s)
The 3rd quartile is calculated as L75=Q3= ( 50+1 )∗75
100 =38.25 ≈38
The value of the 38th number = 705 ($000s)
Part c
The value of the 70th percentile is the value of the 36th individual in the sample. The 36th
number in the sample is $645.55 (000s). Thus, it can be said that 70% of the houses sold have a
price less than or equal to $645.55 (000s).
Part d
The inter-quartile range is calculated IQR=Q3 −Q1=7 05−420.5=284 .5
Hence, it can be said that the middle 50% of the houses having a selling price range of
$284.5 (000s), from 420.5 to 705 ($000s).
TASK 4
Part a
The table below presents the descriptive statistics of the Sold Prices.

9BASIC BUSINESS STATISTICS
Sold Prices (V7)
Mean 620.66
Standard Error 63.86
Median 459.5
Mode 450
Standard Deviation 433.13
Sample Variance 187599
Kurtosis 10.96
Skewness 3.02
Range 2498
Minimum 152
Maximum 2650
Sum 28550.55
Count 46
Confidence Level(95.0%) 128.62
Part b
IFUL=Q3 +1.5∗IQR
¿ 7 05+1.5∗284 .5=7 05+4 26 .7 5=1131.75
IFLL=Q1−1.5∗IQR
¿ 420.5−1.5∗284.5=420.5−4 26.7 5=−6.2 5
Part c
Part i
The calculations done in part “b” are based on quartiles. While the 3rd Quartile is used in
“IFUL”, 1st Quartile is used in “IFLL.” The 3rd Quartile measures the 75th percentile and 1st
quartile measures the 25th percentile. Hence, an appropriate measure of central tendency based on
“part b” would be the median which measures the 50th percentile. The median value of the sold
prices is $459.5 (000s).
Part ii
The inter-quartile range is a suitable measure of dispersion. It is used to measure the
spread of the sold prices of the houses of the middle 50%. The inter-quartile range is $284.5
(000s)

10BASIC BUSINESS STATISTICS
TASK 5

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Part a
Sold Prices (V7)
Mean 620.66
Standard Error 63.86
Median 459.5
Mode 450
Standard Deviation 433.13
Sample Variance 187599
Kurtosis 10.96
Skewness 3.02
Range 2498
Minimum 152
Maximum 2650
Sum 28550.55
Count 46
Confidence Level(95.0%) 128.62
In a normal distribution the mean, median and mode are equal. From the above table it is
seen that the mean ($620.66*1000) house price is more than the median ($459500). Hence the
data is positively skewed. Moreover, the skewness value is also 3.02. Thus the above statement
is justified.
Part b
From the standard normal table
P ( z←1.5 )=0.0668
P ( z>1.5 )=0.9332
Thus, P (−1.5< z <1.5 )=0.9332−0.0668=0.8664 ≈ 0.87
Thus 87% of the samples would fall within ±1.5 standard deviations
Part c
The mean sold price = $620.66 (000s)
The standard deviation of the sold price = $350.69 (000s)
Hence, the upper limit = 620.66+1.5∗433.13 ≈ 1 27 0
The lower limit = 620.66−1.5∗433.13 ≈−29
From the sample data it is seen that there are 42 houses of the 50 houses which are
between $0 (000s) and $1270 (000s). Thus, it is seen that 84% of the houses lie within the limits.

12BASIC BUSINESS STATISTICS
Hence, it can be said that the sold prices are normally distributed.
TASK 6
Part a
Part i
Sold Prices (V7)
Mean 620.66
Standard Error 63.86
Median 459.5
Mode 450
Standard Deviation 433.13
Sample Variance 187599
Kurtosis 10.96373
Skewness 3.02
Range 2498
Minimum 152
Maximum 2650
Sum 28550.55
Count 46
Confidence Level(90.0%) 107.25
The point estimate of the Sold Prices is $620.66 (000s)
Part ii
The lower limit of the confidence interval = 6 20.66−107.25=51 3.41
The upper limit of the confidence interval = 6 20.66+1 07.25=7 27.91
Thus the 90% confidence interval = 513, 728
Part iii
From the above calculation it can be said that when another sample of 50 houses is taken
then there is 90% chance that the mean sold price would lie between $513000 and $728000.
Part b
The upper and lower bounds of 90% confidence interval are $513 and $728 (000s). Since,
the mean sold price ($650000) lies within the confidence interval hence the bounds are
satisfactory.

13BASIC BUSINESS STATISTICS
TASK 7
Part a
The proportion of Brick Veneer Buildings in the sample is 38%
Building Type (V4)
Mean 0.38
Standard Error 0.07
Median 0
Mode 0
Standard Deviation 0.49
Sample Variance 0.24
Kurtosis -1.81
Skewness 0.51
Range 1
Minimum 0
Maximum 1
Sum 19
Count 50
Confidence Level(99.0%) 0.19
Part i
The point estimate for the proportion of Brick Veneer Buildings = 0.38
Part ii
The lower limit of the 99% confidence interval ¿ 0. 38−0.19=0. 1 9
The upper limit of the 99% confidence interval ¿ 0.38+0.19=0.5 7
Part b
The lower limit for 95% confidence interval = 0. 38−1.96∗0.07=0. 38−0.14=0.2 4
The upper limit for 95% confidence interval = 0. 38+1.96∗0.07=0.38+ 0.14=0.5 2
Part c
From the above calculations it is seen that the 99% confidence interval is more wide as
compared to 95%. Thus, it can be said that the lower the confidence interval the more the
precision.

14BASIC BUSINESS STATISTICS
The change in precision is natural between the two intervals since the level of confidence
affects the precision.