Statistics

ASSIGNMENT SUBMISSION FORM Course Name: SMMD Assignment Title: Assignment 1 (HousePrices.jmp)
Submitted by: Garima Agrawal (Section D)
(Student name or group name) Group Member Name | PG ID | Garima Agrawal | 61410506 |

Question1: The data for home values has a considerable wide range (429578) as compared to the inter-quartile range (93522). This means the data has a huge spread and the same can be verified from coefficient of variation which is even more than 41%. Besides, as can be seen from graphical plot and the positive skewness (0.87) measure, the data is skewed towards right. Also, the outliers present towards the right end indicate the presence of few extremely high valued houses, due to which average price of houses is higher than the median price. The highest density of data is present in two lower quartiles, as can be seen from box plot. This shows that low valued houses are present in bulk, and thus must available in the market easily. | |
Question 2: Though normal distribution model is not an absolutely apt for the data set of prices, the data can still be analyzed by assuming normality owing to the fact that data points hover around the diagonal line of normal Quantile plot. Some data points also cross the permissible range, but the density of data (high in the middle, and low at the ends ) allows for the usage of normal distribution model.The same can be verified from the measure of Kurtosis (0.7) which is well in permissible range for usage of normal distribution model. | |

Question 3:

MEAN = 164K; STANDARD DEVIATION = 68K A.Z1 (@ x as 92.8K) = (92.8 – 164)/68 = -1.04Z2 (@ x as 255.5K) = (255.5 – 164)/68 = 1.34P(Z1 < Z < Z2) = 0.9099 – 0.1492 = 0.7607Percentage probability is 76.07, which seems to be more than the actual value, basis what can be seen via boxplot. | B.Z1 (@ x as 232K) = (232 – 164)/68 = 1P( Z < Z1) = 0.8413Percentage probability is 84.13, which is consistent with what can be seen via data distribution. | C.Prob (Z < Z1) = 0.75Z1 = 0.6745Price, X1 = (68)*(0.6745) + 164 = 209.86So, Theoretical value of house at 75th quartile is 209.9K as compared to the actual value of 205.3K. |

Question 4: On the analysis of data set, histogram clearly depicts the presence of white spaces in the data, which are values of living area unavailable in the market. Same is not directly evident from box plot.And the box plot on the other hand aptly shows the position of median and quartiles instantly. As can be seen from histogram as well as box plot, the data set is skewed towards right. The same can be verified from the measure of Skewness (0.807) which being positive indicates a right skewed data set. | |

Question 5:

On the analysis of data set, histograms clearly depict that original variable is a better fit for normal distribution variable as compared to the logarithmic one. The value of kurtosis for the new variable is -0.47 as compared to that of original at 0.392. Closer to zero is the value of Kurtosis, more is the normality in data.In my opinion, this change in normality is due to the fact that logarithm has scaled down the range and thus increased the number of bars relatively. This has caused data to deviate a little from normality. | Plot for living area | Plot for Log(Living Area) |