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Statistics Mae 256 T2 2017 Assignment

   

Added on  2020-02-24

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STATISTICSMAE 256 T2 2017 ASSIGNMENTSTUDENT ID[Pick the date]
Statistics Mae 256 T2 2017 Assignment_1
Question 1The descriptive statistics related to the price has been computed using Excel and summarized ina tabular format below.Interpretation of summary statistics Mean- The mean represented in the table captures the household average price that has beencomputed taking into consideration the sample provided and it comes out as $ 804,880. Althoughmean is a popular central tendency measure but it tends to give a valid result only when theoutlier presence is low. Considering the various summary statistics, it would be fair to concludethat mean presents a fair indication of the central tendency in the given case.Median- Another popular central tendency measure is median which highlights the data valuewhich marks that 50% of the observations would not exceed the selected value. For the givendata, the median value has computes as $ 798,960. This highlights the fact that for the house sale1
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price presented, 50% of these have sold lower than the median value of $ 798,960. When theskew in the distribution is minimal, there is convergence of the median and mean value whichseems to be illustrated to some extent in the given case.Standard deviation – One of pivotal measures to capture variation is the standard deviationwhich is an absolute measure. It is essential that standard deviation must be interpreted alongwith the mean value so as to lead to a valid conclusion with regards to dispersion. For the sellingprice of houses whose data is available, standard deviation has come out as $137,130 and whenviewed along with the mean, it is apparent that dispersion in the selling price of house seems onthe lower side. This conclusion also tends to be derived on the basis of other indicators ofdispersion in the data.Skewness- A crucial indicator with regards to the distribution shape is the skew observed in thedata. For a normal distribution this skew ought to be zero. Further, the presence of skew impliesthat a tail would be present whose respective side is driven by the sign of the skew coefficient. Inthe given case, skew value is 0.09 and hence only a small tail on the right would be visible.Question 2 The value of mean for the sale prices of houses ($ 000’s) ́x=804.88The value of standard deviation for the sale prices of houses ($ 000’s) s=137.13Proportion of houses with the sale prices within 1-standard deviation from the mean value =?The upper and lower range of 1-standard deviation from the mean value would be computed asgiven below:2
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Upper range of 1-standard deviation from the mean value ¿ ́x+(1∗s)¿804.88+(1∗(137.13))¿942.007Lower range of 1-standard deviation from the mean value ¿ ́x−(1∗s)¿804.88−¿¿667.75Requisite range: (667.75942.007)Further, the total number of houses that lie within the above highlighted price range¿638(¿excel)Sample size (Number of houses) ¿1000Hence, The proportion would be determined as given below:Proportion=(6381000)=0.638Therefore, it can be said that nearly “0.638 proportion of the houses lie within the sale price of 1-standard deviation from the mean value of houses.” 3
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