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11:39 .irl SG C} Using a summary table, you can summarize qualitative data using one qualitative variable classied as \"condition" of cars. As depicted in the above two summary tables, the percentage distribution of 600 hundred Toyota cars is colour coded, labelled and ordered as Below (average), Average, and Above (average) and displayed as a pie chart and a bar chart. Using the pie chart, you can clearly see that more than half of the distribution is in average condition, representing 65.7% of all cars. The remaining 343% of cars is represented by the Below (average) condition, representing 15.8%, and nally, by the Above (average) condition, representing 18,6%. Different colours and sizes of each of the three slices indicate the ease of visual comparison for each condition type. The bar chart depicts the height of each bar to show how each condition of cars is categorically ordered as; Below (average), Average, and Above (average). The length of each bar represents the frequency of value for each category of condition. These frequencies help to see how the variable is distributed amongst the three categories to visually discern differences. It depicts the Below (average) as being the shortest bar (>80), indicating that of the total sample, the least amount of cars have a condition that is characterized as being below average quality. The next bar, is the highest in red, it shows the condition of A cars as being in Average condition. This indicates that the bulk of the cars (>330), have subjectively \"normal", or an \"acceptable quality\" of condition as dened by the auction. Lastly, the Above (average) v category in the orange bar depicts (>93) of cars as being less than, and greater in value compared to the other two categories. The bar chart distribution is helplirl to quickly discern differences between each category. The qualitative data we have are categorized, and are ordered to indicate the type of subjective condition of a car. Despite the fact that both pie charts and bar charts are effective at summarizing data, in this case, it is clear that the pie chart is the best way to discern differences in categories. By using ratio - percentage, it is easier to convey the distribution of its parts to the whole. Since we also have only one variable, \"condition", a pie chart is a more effective way to present your ndings to others about how each category is distributed to the total sample size. It's more effective in telling a story about the major, or even the small fractional portions of a slice. In the above chart, you can see that a majority of the distribution is dedicated to Average conditions. The summary ndings may be used as a supplementary aid in decision making without the need to gather more information that is often needed for a bar chart. It can further help in standardizing any accompanying qualitative data points. For example, it can be a great business intelligence aid to see the distribution of sale prices per each category. Doing so can show discrepancies in price paid for cars based on prices - such as paying below, average, or above average prices. The use of is instrumental, and a better choice if more than one variable exists, as it helps to better show and compare quantities that are not part of a whole - or a single variable. 1(1)) Make a table of the medians, variances, and standard deviations of the prices of the automobiles by condition. Discuss your results. Measures of Central Tendon for 4D Sedan SE Sam le The table above corresponds to the median, standard deviation, and variance price for the categorigl, and ordered variable \"condition". The variable has three categories, ordered in a subjective \"ascending order", corresponding to an ascending order of median cost for each type of condition. The table shows the Below (average) median price is $11750, indicating that those with a condition of \"below" cost less than both, the average condition which has a median of $13600. And costing less than the Above (average) condition car, with a median price of $ 19035. The median price range of $7285 indicates that a signicant price difference exists based on the condition or" the car. All three categories are signicantly deviated from the mean, with the Average condition being least deviated from the mean at $2802.97, in comparison to $3094.00 for Above (average), and with Below (average) being the most deviated. Lastly, all three condition types are signicantly varied in cost (pricing). The least varied is the Average condition with $7856629.6 l, the second varied is the Above condition at $9572842.19 with the net difference of $1 7162 12.58 between the two. The most highest price variance is the Below (average) condition at$11158706.42. When compared to the Average condition, the Below (average) has a net difference of $3 302076.81 11:39 .1 5G g+ .. . Question 1 1(a) Construct a bar chart and a pie chart for the variable "condition" of the cars. Your pie chart should show the category names with the percentage breakdown that is, data labels in percentage. - Should the bar chart also be in percentage rather than # of cars? - Sonia (Maryam) Car Conditions for 4D Sedan SE Sample Below Average 18.6% 15.8% Above 65.7% Car Conditions for 4D Sedan SE Sample 600 Below Average Above 400 Number of Cars 200 Below Average Above Car Conditions Comment on both charts in terms of their distributions. Which chart is better at summarizing your "condition " variable? Give a reason for your answer Using a summary table, you can summarize qualitative data using one qualitative variable classified as 'condition" of cars. As depicted in the above two summary tables, the percentage distribution of 600 hundred Toyota cars is colour coded, labelled and ordered as Below (average), Average, and Above (average) and displayed as a pie chart and a bar chart. Using the pie chart, you can clearly see that more than half of the distribution is in average condition, representing 65.7% of all cars.11:39 .1 5G g+ . . . tendency. Normal Distribution Graph Analysis Normal Distribution Graph of Price 30 Thousands 25 20 Price 15 -Price 10 un The normal distribution graph depicts some extreme values which can be seen by the longer rise and fall for some of the frequencies. This would once again confirm our previous statement of Median being the best measure of central tendency. (iii) Which measure of central tendency is best to represent the "Odometer" data: the mean or the median? (Hint: Use the 10% rule). Discuss your rationale for the choice. Histogram Analysis Histogram of Odometre 120 Series1 100 80 Frequency 60 8 o > 66,670.00 [4.00, 8,504.00] (8,504.00... (17,004.00. (25,504.00.. (34,004.00.. (42,504.00... (51,004.00.. (59,504.00.. Odometer From the histogram of the Odometer, we can see that there are no missing values denoted by the lack of space between the bars. In this case we would prefer to use the Mean as the best measure of central tendency. Normal Distribution Graph Analysis 'Odometer' 200 180 Thousands 160 140 120 Odometer - 8 6 8 8 8 As per the normal distribution graph, we can see that there is an equal distribution of range between the frequencies. Unlike the normal distribution graph for "Price" there are no extreme frequencies recorded as such hence we would conclude that Mean would be the best measure of central tendency.11:39 .1 5G Question 2 (a) Find the measures of central tendency (mean and median) for the two variables: "Price" and "Odometer". (i) Discuss the shape of these two distributions. Price Mean 13555.80 Median 13620 Standard Deviation 3200.70 Histogram of Price 160 140 Series1 120 Frequency - 8 8 8 8 8 [5130, 7130] (7130, 9130] (9130, 11130] (11130, 13130] (13130, 15130] (15130, 17130] (19130, 21130] (17130, 19130) (21130, 23130] (23130, 25130] (25130, 27130] Price The graph above represents the histogram of the prices offered by Toyota. If we connect a curve through the surface of each bar of the histogram we get a bell shaped curve of the range of prices. The X axis represents the price(s) and the y axis represents the frequency. The bell shaped curve confirms that the data is normally distributed. The average (mean) price is at 13555.80 as per our calculation. The median which is at 13620 that is depicted on the graph at the 50th percentile (halfway division). The mode which is the bar that has the most frequently occurring value (largest bar) is between 13130 and 15130 as per our histogram above. The standard deviation which is calculated at 3200.70 represents the width of our curve which also shows us the volatility of the prices. The curve would be positively skewed as the tail of the curve on the right side is longer than the left. Odometer Mean 46823.84 Median 37236 Standard Deviation 33784.45 Histogram of Odometre11:39 II" 50 C} space between the bars. In this case we would prefer to use the Mean as the best measure of central tendency. Normal Distribution Graph Analysis 'Odometer' Thousands '; a E g 909 Odometer n HHHHHH wts-ts-tv-CHs-tv-t ESEERSQERRSQ'333 \"Hr-4r! 04an 101 141 161 201 H a C! 3 As per the normal distribution graph, we can see that there is an equal distribution of range between the frequencies. Unlike the normal distribution graph for "Price\" there are no extreme frequencies recorded as such hence we would conclude that Mean would be the best measure of central tendency. b) Find the measures of variability (range, IQR, variance and standard deviation) for the two variables: "Price" and "Odometer". Compare and comment on their variability. c) Which of the two variables, "Price\" or \"Odometer" is relatively more variable than the other? (Hint: Use the CVs). Include the output as pan of your repon. C V= Standard deviation/Mean Price CV= 3200.697/1355530 = 0.236113= 23.61% Odometer CV= 33784.45/46823.84 = 0.721522= 72.15% As per the calculations above, we can conclude that Odometer is relatively more variable with its CV calculations equal to 72.15% compared to the CV calculated for Price at 23.61% 11:39 Frequency 8 Histogram of Odometre I Seoul . . S' e 9? 5': :3" 8 9 a e e e e e .. a Q" S' 5" c7 5\" a\" Er\" Odometer III' SG E} Similarly to the above graph for the Price, the graph above represents a histogram for the variable \"Odometer." If we connect the surface of the bars, we once again get a bell shaped curve. The X-axis represents the odometer values that are normally distributed given their bell shaped curve and the Yaxis represents the frequency. The mean is recorded at the average point ofthe graph at 46823.84 as per our calculations. The median is at 37260 and is depicted on the graph at the 50th percentile (halfway division). The mode which is the bar that has the most frequently occurring value(s) (largest bar) is greater than 66670. This bar also does not t into our bell curve which could denote values or occurrences that are uncommon or one off. The standard deviation is calculated at 33784.45 which depicts the width of the curve and is representative of the volatility of the odometer values. The curve is once again skewed to the right that is positively skewed due to the mean being located towards the right side of the graph. (ii) Which measure of central tendency is best to represent the \"Price" data: the mean or the median? (Hint: Use 10% rule). Discuss your rationale for the choice. Use either a chart or graph to show the distributions graphically. Histogram Analysis Histogram of Price 160 Is.- no nesl 120 5100 a so g 60 40 D x \\ \\ x \\ x \\ x x x x e s e s e e s e s e e '\\ 9) "v "1 '0 '\\ 9 '5 'H \"I N s'g'c77777?w'3'~ e s s? s? s? s? s? s? s? .5? \\ e e Q Q Q Q Q a From the histogram of the Price, we can see there are some data values that are missing, denoted by the gaps between the bars as well as some of the bars are very small in size representing very low frequencies Due to these reasons, the Median would represent the best measure of central tendency. Norma! Distribution Graph Analysis :ands .r n 8 Normal Distribution Graph of Price