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Learning Team Assignment: Descriptive Statistics – Real Estate Data Part 1

Purpose of Assignment

Using descriptive statistics to organize raw data into a table and to produce graphs based on the organized data. An additional purpose is finding measures of central tendency and dispersion for the data and relating the computed standard deviation to its mean of the data.

Resources Required: Chapters 2, 3, and 4

Grading Guide

*Content*	Met	Partially Met	Not Met	Comments:
Create an Excel spreadsheet with 4 columns of the first 100 single family homes listed, not including condominiums or townhouses.	X
Include each of the following categories in the spreadsheet: Property address, listing price, square footage, and number of bedrooms.	X
Prepare a frequency distribution for listing prices, including relative frequencies.	X
Create your frequency distribution as identified in chapters 2, 3, and 4.	X
Generate a histogram from your frequency distribution, again making sure you are consistent with the rules discussed in Chapter 2.	X
Summarize your findings from your frequency distribution and your histogram.	X
Create either a pie chart or a bar graph of the number of bedrooms in your 100 homes.	X
Calculate measures of central tendency for both listing prices and square footages. Those measures are mean, median, and mode.	X
Determine the quartiles for both listing prices and square footages.	X
Calculate measures of dispersion for both listing prices and square footages. Those measures are range, variance, and standard deviation.	X
Apply Chebyshev’s Theorem and the Empirical Rule to both sets of data.	X			Good job with your analysis. Could improve that indicating how application of these rules affects the type of inferential statistics models that we use.
Compare your findings with your actual data.	X
Conclude whether Chebyshev’s or Empirical Rule is more accurate with each of listing prices and square footages.	X			All accurate. Could improve by stating why these rules are important.
		*Total Available*	*Total Earned*
		7	#/X
*Writing Guidelines*	Met	Partially Met	Not Met	Comments:
The paper—including tables and graphs, headings, title page, and reference page—is consistent with APA formatting guidelines and meets course-level requirements.	X			Do not forget to reference your data sources.
Intellectual property is recognized with in-text citations and a reference page.	X
Paragraph and sentence transitions are present, logical, and maintain the flow throughout the paper.	X
Sentences are complete, clear, and concise.	X
Rules of grammar and usage are followed including spelling and punctuation.	X
		*Total Available*	*Total Earned*
		3	#/X
Assignment Total	#	10	#/X
Additional comments: 95% - Great job!

Real Estate Data Part 1

After completely analyzing the statistical data obtained from Zillow, we were able to identify the number of homes that are available based on the preferences of price, number of bedrooms, location, or square footage. The statistical data obtained makes it visibly easier to obtain historical data as to which homes were most frequently listed, purchased, and the areas that are mostly favored. The ability to organize obtained data into visible statistical data and charts creates a more informed method that can be utilized by anyone in order to make a more informed decision. A business manager who utilizes this method of analyzing collected data on products or customers will gain a better insight into how the company is doing and where changes could be made.

Methodology: Team A created an Excel spreadsheet with 4 columns of 100 single family homes in Fairfax, Virginia utilizing the real estate website Zillow. Team A generated numerous charts and graphs to analyze the data. Below is the results of our findings for: frequency distribution; histogram of the frequency distribution and a summary of the finding; bar graph of number of bedrooms and a summary of the graph; calculations of central tendency for listing prices and square footage that include mean, median and mode; quartiles for both listing prices and square footages; dispersion for listing prices and square footages to include range, variance, and standard deviation; applied Chebyshev’s Theorem and the Empirical Rule and compared findings to actual data; and conclude whether Chebyshev’s or Empirical is more accurate.

List of 100 Single Family Homes

Table 1: Data Comment by Mark Freeman: You do not need to show me your data on your analysis report. That’s why you included your spreadsheet.

address	listing price	Sqft	beds
4480 Market Commons Dr Unit 411, Fairfax, VA	262000.00	679	1
2655 Prosperity Ave Apt 205, Fairfax, VA	310000.00	720	1
12112 Garden Grove Cir unit 402, Fairfax, VA	229900.00	832	1
12006 Golf Ridge Ct Apt 201, Fairfax, VA	219000.00	988	2
3800 Green Ridge Ct Apt 102, Fairfax, VA	249900.00	988	2
4412 Helmsford Ln Apt 101, Fairfax, VA	259900.00	1,038	2
4314 San Juan Dr, Fairfax, VA	509000.00	1,080	4
12897 Grays Pointe Rd Unit C, Fairfax, VA	249750.00	1,100	2
12112 Green Leaf Ct Apt 202, Fairfax, VA	262500.00	1,100	3
12926 Grays Pointe Rd Unit C, Fairfax, VA	289900.00	1112	2
4108 Monument Ct unit 102D, Fairfax, VA	275000.00	1,130	2
4212 Lamarre Dr, Fairfax, VA	445000.00	1199	4
11576A Cavalier Landing Ct unit 901A, Fairfax, VA	315000.00	1228	2
4600 Superior Sq, Fairfax, VA	309900.00	1230	2
12321 Strong Ct Unit 569, Fairfax, VA	289900.00	1,259	2
2903 Saintsbury Plz Apt 405 , Fairfax, VA	369900.00	1,264	2
11963 Glen Alden Rd , Fairfax, VA	399500.00	1280	3
11810 Rockaway Ln, Fairfax, VA	365000.00	1,288	2
2904 everleigh Way, Fairfax, VA	398000.00	1,290	3
10329 Sager Ave, Fairfax, VA	329000.00	1,294	2
5536 Starboard Ct, Fairfax, VA	429900.00	1,298	4
3143 Highland Ln, Fairfax, VA	669000.00	1,301	3
13160 Morning Spring Ln, Fairfax, VA	525000.00	1,316	4
4713 Groves Ln, Fairfax, VA	521000.00	1,335	3
3902 Golf Tee Ct Apt 301, Fairfax, VA	310000.00	1,336	3
4135 Fountainside Ln Unit C001, Fairfax, VA	320000.00	1,370	3
9522 Stevebrook Rd, Fairfax, VA	589999.00	1,388	5
5546 Falmead Rd, Fairfax, VA	425000.00	1,452	4
3860 Mohr Oak Ct, Fairfax, VA	434900.00	1,452	3
5431 Crows Nest Ct, Fairfax, VA	389900.00	1,464	3
4311 Chariot Ct Unit 122, Fairfax, VA	411000.00	1,536	3
3601 Jean St, Fairfax, VA	489900.00	1544	5
5580 Glasgow Woods Ct, Fairfax, VA	360000.00	1570	3
5029 Portsmouth Rd, Fairfax, VA	585000.00	1,577	4
1297 Ridgemist Ln, Fairfax, VA	364900.00	1584	3
9901 Comonwealth Blvd, Fairfax, VA	560000.00	1,590	4
5021 Wheatstone Dr, Fairfax, VA	575000.00	1590	4
5218 Concordia St, Fairfax, VA	599000.00	1,596	4
3510 Wilson St, Fairfax, VA	649900.00	1650	4
12249 Fairfield House Dr Unit 412 B, Fairfax, VA	319900.00	1,660	2
4258 Fox Lake Dr, Fairfax, VA	445000.00	1,664	3
4674 Buckhorn Rdg, Fairfax, VA	529000.00	1672	3
3608 Buckeye Ct, Fairfax, VA	419900.00	1,688	3
11015 Braddock Rd, Fairfax, VA	699900.00	1,761	4
10607 Judicial Dr, Fairfax, VA	1500000.00	1,770	3
5506 Ridgeton Hill Ct, Fairfax, VA	434000.00	1,800	4
11519 Rothbury Sq, Fairfax, VA	520000.00	1888	3
12418 Cedar Lakes Dr, Fairfax, VA	469000.00	1,900	4
3005 Cedar Ln , Fairfax, VA	699900.00	1901	4
9211 Gleenbrook Rd, Fairfax, VA	749900.00	1,915	5
3683 Old Lee Hwy , Fairfax, VA	599900.00	1,920	4
4220 Minstrell Ln, Fairfax, VA	500000.00	1,959	4
12785 Dogwood Hills Ln, Fairfax, VA	469900.00	1,960	3
10328 Sager Ave Unit 123, Fairfax, VA	643800.00	2,024	3
3053 Waterloo Ln, Fairfax, VA	724990.00	2,029	3
4503 Monmouth St , Fairfax, VA	590000.00	2,046	3
5779 Sidney Street, Fairfax, VA	394000.00	2,059	4
4174 Rush St, Fairfax, VA, Fairfax, VA	619900.00	2,064	3
11413 Sunflower Ln, Fairfax, VA	520000.00	2,090	3
4427B Beechstone Ln, Fairfax, VA	399900.00	2,188	3
4124 Kentmere Sq, Fairfax, VA	525000.00	2222	2
13120 Pavilion Ln, Fairfax, VA	550000.00	2,231	4
10509 Providence Way, Fairfax, VA	609999.00	2,252	4
12000 Ashford Green Dr, Fairfax, VA	559900.00	2,256	3
4518 Billingham St, Fairfax, VA	539900.00	2264	3
2909 Cedarest Rd, Fairfax, VA	709000.00	2272	4
3133 Robert Evans Dr, Fairfax, VA	615000.00	2,300	4
4807 Bentonbrook Dr , Fairfax, VA	799999.00	2,377	5
12608 Victoria Station Ct, Fairfax, VA	449000.00	2,392	2
3636 Elderberry PL, Fairfax, VA	600000.00	2,394	4
3888 University Dr, Fairfax, VA	499990.00	2400	4
10430 Calumet Grove Dr, Fairfax, VA	524900.00	2,400	4
4058 Laar Ct, Fairfax, VA	649900.00	2,400	4
4820 Twinbrook Rd, Fairfax, VA	564900.00	2,408	4
3003 Rose Arbor Ct, Fairfax, VA	775000.00	2,468	4
4018 Roberts Rd, Fairfax, VA	550000.00	2,523	4
5739 Walcott Ave, Fairfax, VA	599900.00	2,548	4
12453 Blissful Valley Dr, Fairfax, VA	590000.00	2,612	4
5418 Rumsey PL, Fairfax, VA	624900.00	2,685	4
4009 Murdstone Ct, Fairfax, VA	469900.00	2688	3
9713 Dansk Ct, Fairfax, VA	739900.00	2,705	4
13083 Autum Willow Dr, Fairfax, VA	689900.00	2750	5
3515 Wilson St, Fairfax, VA	674900.00	2798	3
3124 Robert Evans Dr, Fairfax, VA	799900.00	2,912	4
3023 Steven Martin Dr, Fairfax, VA	649900.00	3,000	4
11808 Valey Rd, Fairfax, VA	749000.00	3,168	4
3273 F Tilton Valley Dr, Fairfax, VA	775000.00	3213	4
13129 Willoughby Point Dr, Fairfax, VA	644500.00	3,234	4
3609 Jean St , Fairfax, VA	530000.00	3,240	4
12909 Chalkstone Ct, Fairfax, VA	750000.00	3,664	4
3453 Barristers Keepe Cir, Fairfax, VA	829900.00	3,722	4
10092 McCarty Crest Ct, Fairfax, VA	875000.00	3,759	4
4216 Whiteacre Rd, Fairfax, VA	787500.00	3,846	6
3401 Franklin Manor, Fairfax, VA	775000.00	3,902	4
5013 Ox Rd, Fairfax, VA	1190000.00	4,005	4
3554 Early Woodland Pl, Fairfax, VA	1399000.00	4,041	4
12618 Lake Normandy Ln, Fairfax, VA	789000.00	4672	5
3411 Fawn Wood Ln, Fairfax, VA	129900.00	5,589	4
4900 Finchem Ct , Fairfax, VA	949000.00	5677	5
10120 Ratcliffe Manor Dr, Fairfax, VA	1225000.00	6,614	5

Frequency Distribution

Findings:

Listing Price Frequency Distribution
Bin Comment by Mark Freeman: What is this?	Frequency
120000	0
200000	1
300000	10
400000	16
450000	9
500000	6
600000	24
650000	9
700000	5
750000	6
800000	7
900000	2
1000000	1
1200000	1
1500000	3
More	0

Histogram of Frequency Distribution

The frequency distribution and histogram show that the most common homes are in the $400,000 and $600,000 price range. 25 percent of the houses are in the $600,000 and can be visually seen on the Histogram. Comment by Mark Freeman: Good start, but you need to comment on the distribution. Is it skewed? Does it appear to be a normal distribution?

Bar Graph of Bedrooms

Out of 100 homes 45 of them have 4 bedrooms and 28 of them have 3 bedrooms. The chances of finding a home with 2 or more bedrooms in Fairfax, Virginia are 88 percent.

Central Tendency for Listing Price and Square Footage

Listing Price	Median	Mode	Mean
	$529,500.00	$649,900.00	$555,558.27
SQFT	Median	Mode	Mean
	1917.5	2400	2146.09

Quartiles for Listing Price and Square Footage Comment by Mark Freeman: This is great. Could be improved by plotting the quartiles to illustrate.

Quartiles for Price	Minimum Value	1st Quarter	Median	3rd Quarter	Maximum Value
	$129,900.00	$399,125.00	$529,500.00	$654,675.00	$1,500,000.00

Quartiles for SQFT	Minimum Value	1st Quarter	Median	3rd Quarter	Maximum Value
	679	1361.5	1917.5	2481.75	6614

Dispersion for Listing Price and Square Footage

Dispersion for Price	Range	Variance	Standard Deviation
	129900 - 1500000	54904456931	234317.0009

Dispersion for SQFT	Range	Variance	Standard Deviation
	679 - 6614	1139142.77	1067.306315

Chebyshev’s and Empirical Rule Comment by Mark Freeman: You present great information and quantitative analysis. You just to go one step further and explain why all of this is useful. That is, to explain the dispersion of the data so that we can know what type of models we should use in inferential statistical analysis.

Listing Price

Mean	$ 558,523.51
Variance	$ 4,904,456,931
Range	$ (100,000.00)
Standard Deviation	$ 233,616.08


Chebyshev's theorem is a theorem that allows us to approximately know how much percentage of a data set lies within a certain number of standard deviations of the mean of the data set.
	The formula - 1-1/k2 with K=2 at least 75% of the population lies within 2 standard deviations from the mean.
Answer	$ 1,025,755.66	96%
	$ 91,291.35

Empirical Rule	x-s	$ 324,907.43	88
	x+s	$ 792,139.58

	x-2s	$ 91,291.35	96
	x+2s	$ ,025,755.66

The Empirical rule states that a normal distribution should fall between 68.26 and 95.44% of the mean. Since the listing price has a positive skew the normal distribution does not fall within these ranges. The listing price has a huge variance with outliers such as the $1.5 million home. The Empirical rule would be close to the actual distribution then the Chebyshev’s theorem.

Square Footage

Mean	2146
Variance	1139143
Range	5935
Standard Deviation	1067

Chebyshev's theorem
The formula - 1-1/k2	with K=4 at least 93% of the population lies within 2 standard deviations from the mean.
Answer	4281	93
	11

Empirical Rule	x-s	1079	82
	x+s	3213

	x-2s	11	93
	x+2s	4281

The Empirical Rule states that a normal distribution should fall between 68.26% and 95.44% of the mean. The actual numbers are within 5 standard deviations from the mean at 93%. Chebyshev’s theorem is more accurate.

Conclusion

References

Lind, D., Marchal, W., & Wathen, S.A. (2015). Statistical techniques in business & economics (16th ed.). McGraw-Hill. 9780078020520

You forgot to place your data source here. From where did you collect the home price and features data?

Bedrooms

Frequency 1 2 3 4 5 6 More 3 15 28 45 8 1 0

Rooms

Houses

Histogram of Listing Price Frequency

Frequency 120000 200000 300000 400000 450000 500000 600000 650000 700000 750000 800000 900000 1000000 1200000 1500000 More 0 1 10 16 9 6 24 9 5 6 7 2 1 1 3 0

Bin

Frequency