a. Is the standard deviation a useful statistic for describing the dispersion of sales prices? Explain...
a. Is the standard deviation a useful statistic for describing the dispersion of sales prices? Explain
b. Comment on the Shape of the Distribution of Prices
c. Write a description of the Distribution (Bed Rooms)
(Scroll all the way down, there is 2 tables, the first one with some statistical data from the Price table, and the second is for the Bedrooms)
Home Prices:
| Prices |
| $ 167,962.00 |
| $ 169,000.00 |
| $ 174,528.00 |
| $ 175,823.00 |
| $ 183,920.00 |
| $ 188,799.00 |
| $ 189,984.00 |
| $ 190,032.00 |
| $ 190,291.00 |
| $ 194,238.00 |
| $ 195,257.00 |
| $ 199,448.00 |
| $ 200,928.00 |
| $ 202,598.00 |
| $ 206,424.00 |
| $ 209,292.00 |
| $ 214,910.00 |
| $ 216,720.00 |
| $ 218,862.00 |
| $ 225,750.00 |
| $ 226,054.00 |
| $ 226,498.00 |
| $ 228,810.00 |
| $ 229,990.00 |
| $ 230,121.00 |
| $ 237,120.00 |
| $ 240,115.00 |
| $ 241,920.00 |
| $ 246,820.00 |
| $ 248,400.00 |
| $ 250,090.00 |
| $ 251,269.00 |
| $ 258,120.00 |
| $ 263,160.00 |
| $ 264,160.00 |
| $ 265,440.00 |
| $ 274,482.00 |
| $ 275,033.00 |
| $ 276,000.00 |
| $ 293,700.00 |
| $ 294,086.00 |
| $ 294,357.00 |
| $ 299,730.00 |
| $ 302,720.00 |
| $ 308,000.00 |
| $ 310,622.00 |
| $ 310,877.00 |
| $ 312,863.00 |
| $ 313,200.00 |
| $ 316,210.00 |
| $ 316,827.00 |
| $ 321,320.00 |
| $ 323,417.00 |
| $ 326,695.00 |
| $ 335,610.00 |
| $ 336,000.00 |
| $ 336,300.00 |
| $ 337,144.00 |
| $ 346,150.00 |
| $ 346,421.00 |
| $ 348,528.00 |
| $ 351,520.00 |
| $ 360,960.00 |
| $ 362,710.00 |
| $ 363,792.00 |
| $ 366,350.00 |
| $ 369,533.00 |
| $ 369,978.00 |
| $ 371,956.00 |
| $ 372,360.00 |
| $ 376,146.00 |
| $ 383,081.00 |
| $ 384,020.00 |
| $ 384,420.00 |
| $ 388,960.00 |
| $ 392,554.00 |
| $ 392,904.00 |
| $ 393,557.00 |
| $ 393,584.00 |
| $ 404,538.00 |
| $ 410,592.00 |
| $ 416,120.00 |
| $ 416,160.00 |
| $ 445,740.00 |
| $ 448,800.00 |
| $ 453,913.00 |
| $ 459,950.00 |
| $ 466,560.00 |
| $ 478,675.00 |
| $ 487,494.00 |
| $ 496,100.00 |
| $ 523,584.00 |
| $ 537,900.00 |
| $ 546,084.00 |
| $ 547,596.00 |
| $ 558,342.00 |
| $ 667,212.00 |
| $ 667,732.00 |
| $ 694,430.00 |
| $ 706,596.00 |
| $ 793,084.00 |
| $ 793,656.00 |
| $ 841,491.00 |
| $ 848,420.00 |
| $ 919,480.00 |
|
Mean |
$ 357,026.47 |
|
Median |
$ 323,417.00 |
|
Range |
$ 751,518.00 |
|
Mean ABD |
$ 116,285.26 |
|
Standard Deviation |
$ 160,700.13 |
Bedrooms
| # Bedrooms | Homes Sold |
| 2 | 24 |
| 3 | 26 |
| 4 | 26 |
| 5 | 11 |
| 6 | 14 |
| 7 | 2 |
| 8 | 2 |
| Grand Total | 105 |
Homework Answers
a) Question: Is the standard deviation a useful statistic for describing the dispersion of sales prices? Explain
Answer: In a statistical Theory there is the major role of the Dispersion statistics. from the central tendency, we get the idea about the data i.e on average what is the sales price. or the maximum frequency containing sales price. but if the data set is large then the Central tendency values are gathered towards one of the values in the data; the central tendency fails to describes data appropriately.
The Dispersion statistics are helpful in expressing how much the members of a group differ from the mean value for the group. the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. Therefore standard deviation a useful statistic for describing the dispersion of sales prices.
_________________________________________________________________________________________________
b) the Shape of the Distribution of Prices
the Histogram of the Prices is as follows
here The graph shows that the increasing trend in the Sales Price.
|
Mean |
$ 357,026.47 |
|
Median |
$ 323,417.00 |
The shape of the Distribution is Skewed Left (negatively skewed).
___________________________________________________________________________________________________
c. description of the Distribution (Bed Rooms)
here the graph of Number of Bedroom Versus the House sold is as follows
The graph shows the Negative Trend. i.e. if the Number of Bedroom increases the Homes sold decreases.
the summary statistics are as follows
| Homes Sold | |
| Mean | 15 |
| Median | 14 |
| Mode | 26 |
| Variance | 113 |
| Standard Deviation | 10.63014581 |
| First quartile | 6.5 |
| Second quartile | 14 |
| Third quartile | 25 |
the above graph shows the shape of the Distribution is Skewed right (Positively skewed).
Conclusion:
1. The Minimum Number of Bedrooms then there are high homes sold.
2. The standard deviation is also larger. that why data contains a large variability.
3. The shape of the Distribution is Skewed right (Positively skewed).
___________________________________________________________________________________________________
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