...Quantitative Business Analysis The following is the descriptive statistics for the Motion Picture Industry Case study. The data set provided was used to calculate the median, mean and mode for the gross opening weekend. On the first graph you can see that for the opening gross the graph is skewed to the right so the median is the best central tendency measure rather than using the mean. The median opening gross was 0.39, which means 50% of the opening gross values were less than 0.39 and 50% were above 0.39. The opening gross was 3.43, which indicates a right tail. The kurtosis of the opening gross was 13.81, which indicates a leptokurtic distribution. This skew can be seen on the first histogram. The graphs are attached on the excel file as well. The opening gross range was 108.43, from 0.01 to 108.44. The standard deviation of opening gross was 18.87. The Interquartile Range, which calculates the range for the middle 50% of the values, is used to measure the variability. The Interquartile Range for the opening gross was 12.37. The opening gross outliers were calculated on the box-plot and the extreme values were 108.44 which was Star Wars Episode 2, 102.69 Harry Potter and the Goblet of Fire, 77.06 war of the Worlds, 50.34 Mr. and Mrs. Smith, 48.75 Batman Begins, and 33.90 Wedding Crashers, The values are less than z-score of -3 or larger than z-score of +3 which is why they are considered outliers. War of the Worlds at 77.06, Harry Potter and the Goblet of Fire...
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...Descriptive statistics: Opening Gross: Several central tendency measures (i.e., mean, median, and mode) are calculated for opening gross in the Excel file. As can be seen in the below histogram, opening gross has a right tail (i.e., skewed to the right), so median would be a more appropriate central tendency measure than the mean. The median opening gross was 0.39; 50% of the opening gross values were less than 0.39, 50% were above 0.39. The skewness of opening gross was 3.43 indicating a right tail. The kurtosis of opening gross was 13.81 indicating a leptokurtic distribution. The range of opening gross was 108.43, from 0.01 to 108.44. The standard deviation of opening gross was 18.87. However, because the distribution was skewed, interquartile range (IQR), which is the range for the middle 50% of the values, would be a more appropriate measure of variability. The interquartile range for opening gross was 12.37. Opening Gross Outliers: Based on the box-plot, extreme values were 108.44 (Star Wars: Episode II), 102.69 (Harry Potter and the Goblet of Fire), 77.06 (War of the Worlds), 50.34 (Mr. and Mrs. Smith), 48.75 (Batman Begins), and 33.90 (Wedding Crashers). It is also suggested that values that are less than z-score of -3 or larger than z-score of +3 should be considered outliers. Using that criteria 77.06 (War of the Worlds), 102.69 (Harry Potter and the Goblet of Fire), and 108.44 (Star Wars: Episode II) can be considered outliers. Total Gross: Several central tendency...
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...Descriptives | | Gender | Statistic | Std. Error | Discount | Female | Mean | 1624.57 | 56.376 | | | 95% Confidence Interval for Mean | Lower Bound | 1511.02 | | | | | Upper Bound | 1738.11 | | | | 5% Trimmed Mean | 1619.57 | | | | Median | 1614.50 | | | | Variance | 146197.673 | | | | Std. Deviation | 382.358 | | | | Minimum | 892 | | | | Maximum | 2520 | | | | Range | 1628 | | | | Interquartile Range | 498 | | | | Skewness | .100 | .350 | | | Kurtosis | -.328 | .688 | | Male | Mean | 962.06 | 62.291 | | | 95% Confidence Interval for Mean | Lower Bound | 837.12 | | | | | Upper Bound | 1086.99 | | | | 5% Trimmed Mean | 952.25 | | | | Median | 870.50 | | | | Variance | 209527.261 | | | | Std. Deviation | 457.741 | | | | Minimum | 131 | | | | Maximum | 1990 | | | | Range | 1859 | | | | Interquartile Range | 669 | | | | Skewness | .418 | .325 | | | Kurtosis | -.556 | .639 | Discount Statistics | Discount | N | Valid | 100 | | Missing | 0 | Mean | 1266.81 | Median | 1327.50 | Discount | | Frequency | Percent | Valid Percent | Cumulative Percent | Valid | 131 | 1 | 1.0 | 1.0 | 1.0 | | 189 | 1 | 1.0 | 1.0 | 2.0 | | 336 | 1 | 1.0 | 1.0 | 3.0 | | 339 | 1 | 1.0 | 1.0 | 4.0 | | 361 | 1 | 1.0 | 1.0 | 5.0 | | 410 | 1 | 1.0 | 1.0 | 6.0 | | 419 | 1 | 1.0 | 1.0 | 7.0 | | 421 | 1 | 1.0 | 1.0 | 8.0 | | 532 | 1 | 1.0 | 1.0...
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...Median 2 Mode 2 You can conclude that since the data of variable gender is a qualitative data, the mean therefore cannot be a measure of central tendency. For variable Intrinsic job satisfaction score: Mean 5.32 Mode 5.2 Median 5.3 The data of the variable intrinsic job satisfaction score is recorded in a scale. The Mean, Median and Mode are the good measures of the central tendency. The mean satisfaction score is 5.32 with mode as 5.2 and Median, 5.3. It indicates that the intrinsic job satisfaction results indicate that the employees are most satisfied. For variable Gender: Variance 0.25 Standard Deviation 0.50 For variable Intrinsic job satisfaction score: Variance 0.16 Standard deviation 0.40 Skewness 0.52 Kurtosis 0.95 Range 1.5 Min 4.7 Max 6.2 The above data indicates that the variability in the data of the intrinsic job satisfaction score is about 0.40, the range of the data with minimum value (4.7)...
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...Descriptives Notes Output Created 05-SEP-2012 16:32:29 Comments Input Active Dataset DataSet0 Filter Weight Split File N of Rows in Working Data File 51 Missing Value Handling Definition of Missing User defined missing values are treated as missing. Cases Used All non-missing data are used. Syntax DESCRIPTIVES VARIABLES=Income /STATISTICS=MEAN STDDEV VARIANCE RANGE MIN MAX SKEWNESS. Resources Processor Time 00:00:00.00 Elapsed Time 00:00:00.02 [DataSet0] Descriptive Statistics N Range Minimum Maximum Mean Std. Deviation Statistic Statistic Statistic Statistic Statistic Statistic Three-Year-Average Median Income(2008-2010) 51 $29,453 $36,850 $66,303 $50,734.18 $7,555.310 Valid N (listwise) 51 Descriptive Statistics Variance Skewness Statistic Statistic Std. Error Three-Year-Average Median Income(2008-2010) 57082705.308 .389 .333 Valid N (listwise) EXAMINE VARIABLES=Income /PLOT BOXPLOT STEMLEAF /COMPARE GROUPS /PERCENTILES(5,10,25,50,75,90,95) HAVERAGE /STATISTICS DESCRIPTIVES EXTREME /CINTERVAL 95 /MISSING LISTWISE /NOTOTAL. Explore Notes Output Created 05-SEP-2012 16:32:55 Comments Input Active Dataset DataSet0 Filter Weight Split File N of Rows in Working Data File 51 Missing Value Handling Definition of Missing User-defined missing values for dependent variables are treated as missing. Cases Used Statistics are based on cases with no missing values...
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...36 12.02 11.52 Mean 11.95866667 11.59 Mean 12.02866667 11.75 Mean 11.889 12.05 Mean 12.08133333 11.75 Standard Error 0.040231323 11.82 Standard Error 0.040231323 11.95 Standard Error 0.037824003 12.18 Standard Error 0.037630183 11.9 Median 11.955 11.97 Median 12.025 12.14 Median 11.92 12.11 Median 12.08 11.64 Mode 11.93 11.71 Mode 12 11.72 Mode 11.95 12.07 Mode 12.02 11.8 Standard Deviation 0.220356034 11.87 Standard Deviation 0.220356034 11.61 Standard Deviation 0.207170594 12.05 Standard Deviation 0.206108999 12.03 Sample Variance 0.048556782 12.1 Sample Variance 0.048556782 11.85 Sample Variance 0.042919655 11.64 Sample Variance 0.04248092 11.94 Kurtosis -0.623644142 12.01 Kurtosis -0.623644142 12.16 Kurtosis 0.113237323 12.39 Kurtosis -0.115793556 11.92 Skewness -0.235040087 11.99 Skewness -0.235040087 11.91 Skewness -0.522548654 11.65 Skewness -0.389631587 12.13 Range 0.8 12.2 Range 0.8 12.12 Range 0.86 12.11 Range 0.83 12.09 Minimum 11.52 12.16 Minimum 11.59 11.61 Minimum 11.36 11.9 Minimum 11.64 11.93 Maximum 12.32 12 Maximum 12.39 12.21 Maximum 12.22 12.22 Maximum 12.47 12.21 Sum 358.76 11.92 Sum 360.86 11.56 Sum 356.67 11.88 Sum 362.44 12.32 Count 30 11.83 Count 30 11.95 Count 30 12.03 Count 30 11.93 12.23 12.01 12.35 11.85 11.84 12.06 12.09 11.76 12.07 11.76 11.77 12.16 12.11 11.82 12.2 11.77 12.05 12.12 11.79 12...
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...100.0 | 100.0 | | b) c) d) e) f) Descriptives | | G | Statistic | Std. Error | X | A | Mean | 16.20 | 1.562 | | | 95% Confidence Interval for Mean | Lower Bound | 11.86 | | | | | Upper Bound | 20.54 | | | | 5% Trimmed Mean | 16.17 | | | | Median | 16.00 | | | | Variance | 12.200 | | | | Std. Deviation | 3.493 | | | | Minimum | 12 | | | | Maximum | 21 | | | | Range | 9 | | | | Interquartile Range | 7 | | | | Skewness | .310 | .913 | | | Kurtosis | -.644 | 2.000 | | B | Mean | 12.40 | 1.435 | | | 95% Confidence Interval for Mean | Lower Bound | 8.42 | | | | | Upper Bound | 16.38 | | | | 5% Trimmed Mean | 12.44 | | | | Median | 12.00 | | | | Variance | 10.300 | | | | Std. Deviation | 3.209 | | | | Minimum | 8 | | | | Maximum | 16 | | | | Range | 8 | | | | Interquartile Range | 6 | | | | Skewness | -.299 | .913 | | | Kurtosis | -1.021 | 2.000 | | C | Mean | 14.80 | 1.319 | | | 95% Confidence Interval for Mean | Lower Bound | 11.14 | | | | | Upper Bound | 18.46 |...
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...Problems for skewness Chapter 3 Problems 1. Below is a frequency distribution of earnings of 50 contractors in a country. Regarding this distribution, which statement is correct? [pic] i) Compute the mean, variance, the standard deviation and the Coefficient of variation (CV) of the earnings of these contractors. ii) Compute the skewness of the distribution of earnings of these 50 contractors. iii) Is the distribution positively or negatively skewed? Solutions: |Class Interval|x= Midpoints |Frequency |xf |f(x-[pic])2 |[pic] | |0-10 |5 |2 |10 |1523.5 |-17.74 | |10-20 |15 |7 |105 |2168.3 |-16.1 | |20-30 |25 |12 |300 |693.12 |-2.222 | |30-40 |35 |15 |525 |86.4 |.08747 | |40-50 |45 |8 |360 |1230.1 |6.4339 | |50-60 |55 |6 |330 |3010.6 |28.446 | | | |n = ∑f = 50 |∑xf = 1630 |8712...
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...Course Project: AJ Davis Department Stores Natasha Unaphum MATH533: Applied Managerial Statistics September 10th, 2014 Professor Rolston Introduction: AJ Davis is a department store chain, they are trying to get to know more about their clientele and to further expand their business. A sample of 50 credit customers are selected for this research, information that includes, location (rural, urban or suburban), Income (in $1,000), size (household size), years (number of years lived in that location), and credit balance (customers current credit card balance on the store’s credit card). Discuss your 1st variable, using graphical, numerical summary and interpretation Numerical Summary of Credit Balance are as follows: Mean: 3970.5 Minimum: 1864 Standard Deviation: 931.9 Q1: 3109.3 Variance: 868429.8 Median: 4090 Skew: -0.15043 Q3: 4747.5 N: 50 Max: 5678 The histogram above shows the Credit Balance variable of the 50 customers surveyed. The histogram is almost symmetrical with one outlier which is the credit balance of $2,000. While it being symmetrical you can almost fold the y-axis in half to have it look the same. While observing the histogram, its skewed to the left because of the outlier, and the skew is -.015043. Using the Anderson-Darling Normality Test, the P-value for Credit Balance is 0.400, and A^2 is 0.38. Throughout...
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...Equal Variances). 4. Test whether the average property market value in 2010 is significantly different from those in 2011 at 3% level of significance. Answers: 1. Draw a histogram with properties’ building footages, and their market value in 2011. Discuss the characteristics of those 2 distributions. Answer: The histograms, one shows the properties by their market values while another by their sizes in 2011 are showed below. The values of skewness and kurtosis of the first histogram in Figure 1.1 (that is, by the property market values) are 0.201 and -1.112 respectively, while the values for a normal distribution should be both zero (Table 1.1). The skewness value of 0.201 shows a slight pile-up of scores on the left of the distribution (the mean of $4.62 million is still close to the median of $4.36 million). The kurtosis value of -1.112 (a negative value) indicates the tails of the distributions are lighter than that of normal distribution. Figure 1.1 On the other hand, the values of skewness and kurtosis of the second histogram in Figure...
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...| 410.911 | | | | Upper Bound | 537.104 | | | 5% Trimmed Mean | 461.956 | | | Median | 437.000 | | | Variance | 38923.356 | | | Std. Deviation | 197.2900 | | | Minimum | 169.9 | | | Maximum | 975.0 | | | Range | 805.1 | | | Interquartile Range | 219.1 | | | Skewness | 1.096 | .374 | | Kurtosis | 1.011 | .733 | Sale Price | Mean | 454.223 | 30.4397 | | 95% Confidence Interval for Mean | Lower Bound | 392.652 | | | | Upper Bound | 515.793 | | | 5% Trimmed Mean | 441.219 | | | Median | 417.500 | | | Variance | 37063.085 | | | Std. Deviation | 192.5178 | | | Minimum | 165.0 | | | Maximum | 975.0 | | | Range | 810.0 | | | Interquartile Range | 216.4 | | | Skewness | 1.159 | .374 | | Kurtosis | 1.184 | .733 | Days to Sell | Mean | 106.00 | 8.256 | | 95% Confidence Interval for Mean | Lower Bound | 89.30 | | | | Upper Bound | 122.70 | | | 5% Trimmed Mean | 102.64 | | | Median | 96.00 | | | Variance | 2726.513 | | | Std. Deviation | 52.216 | | | Minimum | 28 | | | Maximum | 282 | | | Range | 254 | | | Interquartile Range | 68 | | | Skewness | 1.078 | .374 | | Kurtosis | 2.022 | .733 | 2. Descriptive Statistics for 18 No Gulf View Condominiums Mean List Price: $ 212805 Mean Sale Price: $203188 Mean Days to Sell: 135 Descriptives | | Statistic | Std. Error | List Price | Mean | 212.806 | 11.5365 | | 95% Confidence Interval for Mean | Lower Bound | 188.466 | | | | Upper...
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...data set used for the analysis: Variable | How the variable is measured | Branch | Branches of the company:1= TESS-Nizhnevartovsk, TESS-Kogalym2= TESS Head Office, TESS-Surgut3=TESS-Tyumen, TESS-Khanty-Mansiysk | Number | Number of the respondent | Work_Exp | Work Experience in JSC “TESS”:1= 2 year or less 2= more than 2 years | JSL | Job Satisfaction Level:Ratings from 1 to 5 where 1= very unsatisfied, 5= very satisfied and 0= no answer/blank | 1.2. Revised Data. Test for Normal Distribution To proceed with the analysis it is necessary to determine if the data are distributed normally. The Histogram below as well as the Descriptive Statistics (Appendix 1, Table 1b) show that the data distribution is leptokurtic (kurtosis is 2,021) and negatively skewed (skewness -,240). We can determine several outliers (Appendix 1, Table 1c, Table 1d) with extreme ratios. In cases #46 and #178 JSL is more than the highest option provided in the questionnaire. That could be a mistake in data entering or the respondent wanted to emphasise his/her satisfaction level. These cases were delisted. Cases with “0” responses are to...
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...LAB 1 –Mohammed Abdo 1.Analyze and discuss the results shown in the Statistics table (including definitions of the following statistical measures: Mean, Std. Error of Mean, Median, Mode, Std. Deviation, Variance, Skewness, Std. Error of Skewness, Kurtosis, Std. Error of Kurtosis, Range, Percentiles) (15%) Statistics | | Variable 1Life expectancy at birth (years), 2006 | Variable 2 Adult literacy rate (% aged 15 and above), 2006 | Variable 2 Combined gross enrolment ratio in education (%), 2006 | Variable 4GDP per capita (PPP US$), 2006 | N | Valid | 179 | 172 | 179 | 179 | | Missing | 1 | 8 | 1 | 1 | Mean | 67.7291 | 83.8767 | 71.5654 | 12258.81 | Std. Error of Mean | .80424 | 1.44937 | 1.33369 | 1066.857 | Median | 71.3000 | 91.2000 | 73.5000 | 6679.00 | Mode | 71.30a | 99.90 | 59.60a | 630a | Std. Deviation | 10.76001 | 19.00828 | 17.84362 | 14273.577 | Variance | 115.778 | 361.315 | 318.395 | 203735005.245 | Skewness | -.901 | -1.378 | -.470 | 1.811 | Std. Error of Skewness | .182 | .185 | .182 | .182 | Kurtosis | -.168 | 1.156 | -.040 | 3.633 | Std. Error of Kurtosis | .361 | .368 | .361 | .361 | Range | 42.20 | 77.10 | 88.70 | 76808 | Minimum | 40.20 | 22.90 | 25.50 | 281 | Maximum | 82.40 | 100.00 | 114.20 | 77089 | Percentiles | 10 | 50.1000 | 54.3300 | 45.1000 | 888.00 | | 20 | 57.8000 | 69.6200 | 57.3000 | 1592.00 | | 25 | 62.0000 | 73.7500 | 60.8000 | 1965.00 | | 30 | 64.5000 | 80.0500 | 63.2000 | 2489.00 | | 40 | 68...
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...University of Great lakes Kisumu Marjorie Adoyo Ogutu BSN/12-M/07 BIOSTATISTICS ASSIGNMENT 1. KURTOSIS The kurtosis of a distribution describes its degree of peakedness or its peakedness relative to the length and size of its tails. A distribution that is relatively flat and has short tails is of low kurtosis and is said to be platykurtic. A distribution with a sharp peak and long tapering tails is of high kurtosis and is termed as leptokurtic. The normal distribution is used for reference or comparison, thus mesokurtic. 2. PERCENTILES AND QUARTILES The percentile of a set of observations divide the total frequency into hundredths i.e,the 30th percentile is that value of the variable below which 30% of the observations lie. The term quartile is a generic term for division point relative to any partition.i.e percentile, tertiles, quartiles and deciles are all examples of quartiles. Therefore a percentile is a rank in percentage while a quartile is a value of the observed variable. 3. BOX AND WHISKER PLOTS Also known as box plots. It entails putting the values in numerical order or arranging from the least to the largest value, and then you find the median of your data. The median divides the data into two halves. You then divide the data into quarters by finding the median of the two halves. Thus Q1-Is the middle number for the first half of the list. Q2-Is the middle number of the whole list. ...
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...Case 2: Gulf Real Estate Properties. Please provide a Managerial Report that includes: 1. Appropriate descriptive statistics to summarize each of the three variables for the forty Gulf View condominiums 2. Appropriate descriptive statistics to summarize each of the three variables for the eighteen No-Gulf View condominiums 3. Comparison of your summary results from #1 & #2. Discuss any specific statistical results that would help a real estate agent understand the condominium market. 4. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. 5. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. Also, consider the following scenario and include your responses in your Report: 6. Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No-Gulf View condominiums with a margin of effort of $15,000. Using 95% confidence, how large should the sample sizes be? GULF VIEW CONDOMINIUMS List Price Sales Price Days to Sell 495000 475000 130 379000 350000 71 529000 519000 85 552500 534500 95 334900 334900 119 550000 505000 92 169900 165000 197 210000 210000 56 975000 945000 73 314000 314000 126 315000 305000...
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