Frequency_Distribution

Frequency Distribution, Measures of Central Tendency and Dispersion The following will include the answers to the assigned questions in week 5. Sevilla & Somers: Activity 18.1 1 Probability distribution which is a function that describe and obtain a list of outcome that is not equal. Frequency Distribution used to calculate the probabilities of getting each outcome. In the first part to toss a coin 10 times and result as follows: |Toss# |1 | |0 |0 + 0 = 0 | |1 |1 + 2 = 3 | |2 |1 + 3 = 4 | |3 |4 + 2 = 6 | |4 |6 + 2 = 8 | |5 |10 + 3 = 13 | |6 |6 + 4 = 10 | |7 |5 + 2 = 7 | |8 |2 + 4 = 6 | |9 |0 + 2 = 2 | |10 |0 + 1 = 1 | 1.d Below is the scatter plot of the total of 60 Tosses from 1.c : [pic] The curve looks like a pyramids or pointed bell where the top point has a value of 13, at the same time the curve is increasing from the point 0 towards the maximum value 13, and then decreasing into the lowest point which is 1. Hence, the curve is centered at “5” and spread from “0 to 10”. 1.e Below is the bar graph from 1.d data [pic] 1.f The hand curve shows similarity to the curve in 1.d with some irregularity due to the un-steady motion of the human hand. Lind, Marshal, & Wathen text: Ch.17, exercise 20 (a and b only) A. Mean chart has two limits: upper control limit (UCL) and lower control limit (LCL) in which control limits are lines in a chart that indicates the upper and lower limits in order to judge the significance of variation in a plotted data. (business dictionary). In calculating the upper/lower control limits, following formula used: LCL/ UCL = X+/-3 and square root of c. where X is the Mean which is the sum of all data values = 2620.9 divided by the total number of data = 30. Therefore, X = 87.3 using the above formula to calculate the lower/upper control limits. Therefore, the LCL = 86.61 and UCL = 88.11 R represent the range, calculating the mean of the range following formula used: LCL/UCL = X +/- A2R, Range which is the highest value minus the lowest value. Therefore the range = 88.5 – 87 = 1.5, therefore, the LCL = 0 and UCL = 2.75 B. The below graph show the plot of the control limits for the mean outside diameter: [pic] The below graph will show the plot of the control limits for the range outside diameter: [pic] Sevilla & Somers: Topic 17, Exploration 2 A. The mean of the year 2000 revenue for the Pennsylvania where the mean equal to total sum of revenue / number of value, therefore, the mean for the year 2000 revenue of the Pennsylvania = 631.25 million. The standard deviation of the year 2000 for the Pennsylvania where the standard deviation is the square root of the variance, therefore, the standard deviation of the year 2000 revenue of the Pennsylvania approximately = 741.6 million. B. The mean of the year 2000 revenue for the Michigan where the mean equal to total sum of revenue / number of value, therefore, the mean for the year 2000 revenue of the Michigan = 110.17 million. The standard deviation of the year 2000 for the Michigan where the standard deviation is the square root of the variance, therefore, the standard deviation of the year 2000 revenue of the Michigan approximately = 195.7 million. C. Comparing the Pennsylvania and Michigan companies in their average revenue, found that Pennsylvania companies average revenue is higher the Michigan’s by three times where mean data values for Pennsylvania are higher. D. If the highest value from both companies removed, Pennsylvania revenue still higher than Michigan revenue where Pennsylvania mean change to 435.71 million, standard deviation to 533.78 million, and Michigan mean change to 168.04 million, standard deviation to 112.12 E. The mean of the number of employees for the Pennsylvania companies equal to 2973.625 and the standard deviation is approximately = 3,978.88 F. The mean of the number of employees for the Michigan companies equal to 739.667 and the standard deviation is approximately = 941. Values of means and standard deviation from (E&F) of the number of employees for both Pennsylvania and Michigan companies shows that Pennsylvania companies employees are almost four time Michigan companies employees. References Business Dictionary, retrieved October 19, from http://www.businessdictionary.com/definition/control-limits.html Lind, D.A., Marchal, W.G., & Wathen, S.A. (2005). Statistical technique in business and economics. (12th ed.). New York: McGraw-Hill. Sevilla, A. & Somers, K. (2007). Quantitative reasoning: Tools for today’s informed citizen. Emeryville, CA: Key College Publishing.