Basic Business Statistics Assignment: Data Analysis and Reporting

This document presents a comprehensive solution to a basic business statistics assignment. The assignment covers various aspects of statistical analysis, including descriptive statistics, frequency distributions, and confidence intervals. It begins with data selection and sampling techniques, followed by the calculation and interpretation of descriptive statistics such as mean, median, mode, standard deviation, and skewness. The solution also includes frequency analysis of building types and the calculation of percentiles and interquartile ranges. Furthermore, the assignment delves into confidence intervals, exploring both point estimates and interval estimations for the mean and proportions. The analysis is detailed, providing step-by-step calculations and interpretations of the results. The document aims to demonstrate a practical application of statistical concepts in a business context, showing how to analyze data, draw meaningful conclusions, and present findings effectively. The assignment is contributed by a student to be published on the website Desklib, which provides all the necessary AI-based study tools for students.

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

2BASIC BUSINESS STATISTICS
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.

4BASIC BUSINESS STATISTICS
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

5BASIC BUSINESS STATISTICS
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

8BASIC BUSINESS STATISTICS
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

11BASIC BUSINESS STATISTICS
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.