Statistics Minor assignment 1 Essay Example

Statistics 8

Subject: STATS1900 Business Statistics

Introduction

This report is an evaluation of customized and not customized houses sold in small and large residential areas over a 3-month period. The aim is to understand the house prices, whether they are custom built and their location. The paper will also scrutinize the variables that may influence house prices. In order to attain this objective, a random sample of 80 houses was obtained from a data of 117 houses.

Random sample

Table 1: The Random Sample

 Location Square Metres 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Basic descriptive statistics and graphs

Table 2: Descriptive statistics for the variable price

Figure 1: Histogram showing house prices

Figure 2: Boxplot of house prices

According to the histogram shown in figure 1, the distribution of house prices is skewed to the right with a long tail stretching rightwards. This is also confirmed by the boxplot in figure 2. The boxplot gives a longer whisker at the upper side hence most values are to the left of mean. It means that the prices of houses are concentrated on the lower end. By further observing the histogram, there is no doubt that the distribution is unimodal with a single clear peak of 243,750. Besides, the distribution does not have outliers since there are no extreme values that differ greatly from other observations.

Given the skewed distribution, the best measure of central tendency is the median. In a skewed distribution, mean is usually dragged in the direction of skewness hence median ought to be used because it is unaffected by extreme values. The median price of houses as given by the descriptive statistics in table 2 is 234,125. In terms of dispersion, semi-interquartile range will be used to indicate spread of house prices. The measure is applied given that it is not sensitive to extreme scores.

The calculated value of semi-interquartile range shows that house prices spread out from the central point by 51,031.

Side-by-side boxplots

Figure 3: Side-by-side boxplots showing the relationship between house price and custom

According to figure 3, the distribution of house prices for both customized and not customized are skewed to the right with a longer tail stretching on the upper side. The second deduction that can be made from the side-by-side boxplot is that customized houses are expensive as indicated by medium value and more spread with a range of 347,500 compared with 330,000 of not customized. In measuring location, median will be used. The boxplots in figure 3 displays customized houses with a higher median location compared with not customized houses. This implies that customized houses are more expensive than not customized houses.

Pivot tables

Table 2: Pivot table comparing custom with location

Table 3: Pivot table displaying relative frequencies

Table 2 below displays a comparison of houses in terms of location and custom. According to the table, small residential area has 22 not customized houses and six customized. On the other hand, large residential area contains 41 not customized houses and 11 customized houses.

In terms of relative frequency, not customized houses make up a bigger percentage of houses in both small and large residential areas. In small residential area, 78.57% of houses are not customized while the remaining 21.43% are customized. This situation is also reflected in a large residential area. In summary, 78.75% of houses in both locations are not customized. This can be compared with 21.25% that are customized.

Conclusion

The first part of the report indicates that the distribution of house prices was skewed to the right. This implies that the distribution of prices are concentrated on the lower end i.e. most houses are cheap with a few expensive houses. From the side-by-side boxplot, customized houses are not only more spread in terms of prices but also expensive compared with not customized houses. The report further sheds light on the distribution of customized and not customized houses in different locations. Evidently, not customized houses are mainly constructed in both small and large residential areas.

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