# Percentile determined informs that approximately 70

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percentile determined informs that approximately 70% of Sold Price values should be less than or equal to \$752,000. Determine the Inter-Quartile Range of your sample “Sold Price” data and provide a brief explanation of what information this statistic provides about your sample data. ( 3 marks ) Inter-Quartile Range=Q 3 –Q 1 = 800-424 = 376(\$000s). The information that can be generated from this is that the middle 50% of Sold Price values are contained within the \$376(\$000s) interval from \$800(\$000s) to \$424(\$000). Task 4 (A) Sold Price (\$000s) Mean 659.63 Standard Error 64.54 Median 602.5 Mode 445 Standard Deviation 428.11 Sample Variance 183282.72 Kurtosis 11.02 Skewness 2.81 Range 2538 Minimum 112 Maximum 2650 Sum 29023.8 Count 44

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(b) Use Excel to produce a Descriptive Statistics table for your sample “Sold Price” Data. IFUL = Q3 + 1.5*IQR = 800+ 1.5*376 =1364 IFLL = Q1 – 1.5*IQR =424 – 1.5*376 = 140 (c) Based on the limits calculated in (b), choose from the numerical summary measures provided in the Descriptive Statistics table, and/or measures calculated previously in Task 3 (i) An appropriate measure of central tendency Median and mode values are used as measures of central tendency since there is the presence of outliers in data. Mean cannot be used as the measure of central tendency as it is affected by the presence of outliers in the data. (ii) An appropriate measure of dispersion for your sample “Sold Price” data. Inter-Quartile Range (IQR) is an appropriate measure of dispersion for the sample sold price data. Task 5 (a) From the Descriptive Statistics table obtained in Task 5, identity three pieces of evidence that indicate whether your sample “Sold Price” data has been obtained from a normally distributed population or not. ANS: Here, the “Sold Price” is not distributed equally due to the following reasons: • Mean isn’t equal to median Mean= 659.63 Median= 602.5 • Skewness isn’t equal to 0. Skewness=2.81 • Histogram is not symmetrical. Sold Price (\$000s) Mean 659.63 Standard Error 64.54 Median 602.5 Mode 445 Standard Deviation 428.11 Sample Variance 183282.72 Kurtosis 11.02 Skewness 2.81 Range 2538 Minimum 112 Maximum 2650 Sum 29023.8 Count 44 UL = 1301.8 LL =17.46
Mea n Standa rd Erro r Median Mod e Stan dar d Dev iation Sample Varia nce Kurtosis Ske wness Range Mi nimum Maxi mum Sum Count 659.6364.54 602.5 445 428.11 183282.72 11.02 2.81 2538 112 2650 29023.8 44 Histogram for sold prices(\$000) Stat Frequency Therefore, the data is not normally distributed. (B) Regardless of your conclusion in above, assume the “Sold Price” population data is normally distributed. Applying the Standard Normal tables, calculate how many “Sold Price” observations in your sample would expect to lie within 1.5 standard deviations of the mean

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