Frequency Column Chart and Relative Frequency Pie-Chart are shown below:
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Frequency Column Chart
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V4
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Building Type
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Frequency
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Relative frequency
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1
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Brick
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12
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0.24
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2
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Brick Veneer
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20
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0.4
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3
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Weatherboard
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15
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0.3
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4
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Vacant land
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3
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0.06
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TOTAL
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50
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1.00
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A total of 12 properties in my sample consist of brick buildings.
The most frequency building type in my sample is brick veneer which accounts for 40% of the total sample or in total 20 buildings.
It is apparent from the relative frequency and also the corresponding pie chart that 30% of the properties in my sample consist of Weatherboard Buildings.
Task 3
- Sold price data (in $ 000’s) is shown below:
- Percentile location formula
- The 70th Percentile
Hence, 70th percentile = 34th value = $ 715,000
The first and third quartiles
First quartile
Hence, first quartile = 12th value = $ 460,000
Third quartile
Hence, third quartile = 36th value = $ 736,000
The 70 percentile tends to represent that 70% of the houses sold would have a price lower than or equal to the corresponding value of 70th Thus, only 30% of the houses have a selling price in excess of $ 715,000 based on the given sample.
The value of Inter- Quartile Range for the variable sold price would be given below:
= $ 276,000
The IQR is a measure of dispersion as it highlights the range of the middle 50% of the values. It is often considered to be a superior metric in comparison to range as the range may be impacted by outliers which is not true for IQR.
Task 4
Descriptive Statistics for sold price is shown below:
The upper and lower inner fence limits based on the IQR and quartile values is computed below:
Based on the above computed limits coupled with the descriptive statistics, it is apparent that the appropriate measure of central tendency would be the median of the sold price. This is because there are some outliers on the positive side which would tend to distort the mean and make it unsuitable as a central tendency measure.
The appropriate variation measure to be used would be IQR since it focuses on the middle 50% of the data and tends to ignore the extreme values which potentially would distort other measures of variation such as standard deviation.
Task 5
Based on the descriptive statistics, it is apparent that the population is not normally distribution. Three piece of evidence which tend to support the above conclusion are represented below.
There is presence of positive skew or right tail while in case of normal distribution the skew is supposed to be zero.
The kurtosis value is not equal to +3 which is the standard value expected for normal distribution.
There is no coincidence of the mean, median and mode which is essential for a normal distribution.
P(Z<1.5) = 0.9332 (based on Z table)
P(Z<-1.5) = 0.0668 (based on Z table)
P(-1.5<Z<1.5) = 0.9332-0.0668 = 0.8664 or 86.64%
Values that would be expected to lie between the Z=-1.5 and Z=1,5 are 86.64% of 47 = 41
Mean – 1,5*standard deviation = 666378-1.5*423435 = $ 31,225
Mean + 1.5*standard deviation = 666378 +1.5*423435 = $ 1,301,530
Based on the given sample of sold price, it is apparent that out of the 47 sold price data available, 44 properties tend to lie in the above range. The answer in the given case is greater than the predicted answer in b) which lends support to the conclusion drawn in (a).
Task 6
- The requisite descriptive statistics for sold price is indicated below.
- The point estimate of the mean sold price would be the mean value itself which is equal to $666,378
- Lower limit of the 90% confidence interval = 666378-103681 = $ 562,696
Higher limit of the 90% confidence interval = 666378-103681 = $ 770,059
There is a 90% chance that the mean sold price of the population would lie between $ 562,696 and $ 770,059.
The value $ 650,000 tends to lie in the 90% confidence interval that is derived above and hence it would be considered a satisfactory value.
Task 7
The descriptive statistics for brick veneer properties is indicated below.
Point proportion of brick veneer properties = 0.40 or 40%
Lower limit of 99% confidence interval = 0.40-0.19 = 0.21
Higher limit of 99% confidence interval = 0.40+0.19 = 0.59
95% confidence interval for brick veneer properties = 0.4 ±96*[(0.4)(1-0.4)/50]0.5 = 0.4 ± 0.069 = (0.3307, 0.4693)
