Assignment_1

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Western University *

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1000A

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Statistics

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Feb 20, 2024

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DS 1000 Assignment 1 – due September 30, 2022 at 11:55 pm • Questions with the computer symbol : must be answered using Python. All code must be provided. • Submissions must be done via Grade scope . You must carefully assign questions to their corresponding pages . Questions with no pages assigned to them will receive zero marks. • Each student must submit their own work . Scholastic offences are taken seriously, and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf Question 1 (20 pts) The tons handled in a year of the 25 busiest ports in the United States (The 2013 World Almanac) are displayed in the histogram below. a. (5 pts) Describe the shape of the distribution. This Histogram has a right skewed distribution because the mean of the data is to the right of the median, and the peak of the graph lies on the left side b. (5 pts) Approximately what percent lies below 75? Approximately 70% of the data lies below 75. I came to this answer by Approximating that there are 25-30 data points and around 18-20 are before 75, therefore I divided 19/16 to get an approximate percent.

c. (5 pts) Approximately what are the minimum and maximum of the data set? Min: 25 Max: 225 The Maximum is of cause of an outlier in this data set because there is only a small amount of data close to the maximum value. (5 pts) What is the center of the dataset? (For this question, take the center to the value with roughly half the years having lower tons handled and half the years having higher tons handled). The Center is around 60-80 and the data ranges from approximately 25-225. Although there is not much data corresponding with the 225, meaning could have an outlier. Question 2 (20 pts) An article reported on a study of strength properties of high-performance concrete obtained by using superplasticizers and certain binders. The data below shows the flexural strength (a measure of ability to resist failure in bending) in MegaPascals. 5.9 7.2 7.3 6.3 8.1 6.8 7 .0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7 a. (5 pts) Make a stem plot. Be sure to label the units. Leaf unit: 0.1 Stem Leaf 5 9 6 33588 7 0023467788 8 127 9 077 10 7 11 368 b. (5 pts) Describe the shape, center, and variability of the distribution. Shape: The shape of this graph is slightly skewed to the right, almost symmetrical Center: the center is in between data points 7.7 and 7.7

Variability of distribution: The spread of the data ranges from 5.9 -11.8, and decimal places c. (5 pts) Without using software, calculate the mean and median of these data. Show your work. Compare these two values. What do they tell you about the distribution? SCAN Mean: 8.15 Median: 7.7 Difference: 0.45 The two values are very close in value meaning the distribution is positive as well as only slightly skewed to the right. The 0.45 represents the skew in the distribution. d. (5 pts) Without using any software, calculate the first and third quartiles of these data. Show all your work. Min: 5.9 Q1: 7.0 Median: 7.7 Q3: 8.7 Max: 11.8 SCAN CALCULATIONS

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Question 3 (15 pts) Home sale amounts were reported for a sample of homes in Almeda, CA, that were sold the previous month (1000s of $). 590 815 608 350 1285 408 540 555 679 a. (5 pts) Calculate the mean and standard deviation. 350, 408, 540, 555, 590 , 608, 679, 815, 1285 xi Deviations xi - x Squared deviations Squared deviation 350 (350-647.7) (-57.7) *2 3329.2 408 (408-647.7) (167.3) *2 27 989.2 540 (540-647.7) (-39.7) *2 1576 555 (555-647.7) (-29.77) *2 886.25 590 (590-647.7) (637.3) *2 406 151.2 608 (608-647.7) (-239.7) *2 57 456 679 (679-647.7) (-107.7) *2 11 599 815 (815-647.7) (-92.7) *2 8593.2 1285 (1285-647.7) (31.3) *2 979.6 518 559/8 = 64 819.8 64 819.8 =   = 254.59 b. (5 pts) Calculate the median and range. c. (5 pts) Which measurements would you suggest using for this data set? Explain? $1000 of dollars.

Question 4 : (5 pts) A soft drink machine has 5 options to choose from: Coca-Cola, Dr. Pepper, Sprite, Diet Coke, and Pepsi. A sample of 50 soft drink purchases is selected, and the proportion of each selection is shown below. Soft Drink Percentage % Coca-Cola 38 Diet Coke 16 Dr. Pepper 10 Pepsi 26 Sprite 10 Make a pie chart to display the distribution of soft drink purchases. Choose the colours so that Coca-Cola is brown, Diet Coke is white, Dr. Pepper is red, Pepsi is blue, and sprite is green. Question 5 : (15 pts) Smartphones are advanced mobile phones with Internet, photo, and music and video capability. The following survey results show smartphone ownership by age.

Smart phone Other Cell Phone No Cell Phone Age 18-24 49 46 5 25-34 58 35 7 35-44 44 45 11 45-54 28 58 14 55-64 22 59 19 65+ 11 45 44 a. (5 pts) The first row gives percentages of cellphone ownership for ages 18-24. Using this information, draw a bar chart. b. (5 pts) Draw a bar chart that illustrates the smartphone ownership for each age group. Use a bidimensional bar chart.

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c. (5 pts) Using the barcharts in part a. and b. give a simple description of the changes in cellphone ownership for the different age groups.

Question 6 : (15 pts) (dataset LargeCorp.csv) Fortune provides a list of America’s largest corporations based on annual revenue. The data describe the 50 largest corporations with annual revenue expressed in billions of dollars. a. (5 pts) Make a histogram of these data. b. (5 pts) What is the shape of the distribution? How many of the corporations have annual revenue more than 100 billion dollars? The shape of the distribution is very skewed to the right with the majority of the data being before 150. I have made that observation by the way the graph looks visually, as well as looking at the range between 43- 443, which equals to 400, that means there are outliers.

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c. (5 pts) From the histogram, what is the minimum and maximum annual revenue? What is the centre? Question 7 : (10 pts) (Cholesterol.csv) A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped. Give a graphical comparison of the cholesterol distributions for the two groups using side- byside boxplots. Provide appropriate numerical summaries for the two distributions and identify any outliers in either group. What can you say about the effects of smoking on cholesterol levels?