Introduction to Statistics and Graphical Descriptive Measures

Questions: A. politician who is running for the office of mayor of a city with 55,000 registered voters commissions a survey. In the survey, 52% of the 250 registered voters interviewed said they plan to vote for her.i. Describe the population of interest? ii. Describe the sample? iii. Is the value 52% a parameter or a statistic? Explain your answer.B. At the Eastern Suburbs Community College, administrators want to determine the average commuting distance for their students. They randomly select 350 students who commute and ask them the distance of their commute to campus. From this group a mean of 15.5km has been calculated.i. Describe the parameter.ii. Describe the statistic. iii. Describe the population.Question 2 a. Define each of the following Types of Data: i. Nominalii. Ordinaliii. Intervalb. For each of the following, identify the data type as Nominal, Ordinal, or Interval. i. The size of an order of fries (small, medium, large) purchased by a fast food customer.ii. The reading of the odometer of a motor vehicleiii. The marital status of respondents in a Customer Satisfaction Surveyiv. The extent to which a Customer agrees (Strongly Agrees, Agrees, Neutral, Disagrees, StronglyDisagrees to a Statement regarding the Companys refund policy is fairv. A students STAT201A Mid-Trimester Examination result as a percentagevi. A students STAT201A Mid-Trimester Examination result as a Grade (Fail, Pass, Credit, Distinction, High Distinction)Question 3 To help determine the need for more Golf Courses, a survey was undertaken. A sample of 60 self-declared Golfers we asked how many rounds of golf they played last year. The data collected is as follows: 18 15 25 18 29 28 23 20 13 26 29 24 3 13 28 26 18 30 24 23 9 20 30 26 17 18 30 28 18 19 35 18 14 25 19 28 28 12 30 36 31 13 14 14 42 30 29 20 18 27 25 36 31 29 24 36 23 24 16 22 a. Draw /Construct a correctly labelled Histogram b. Draw /Construct a correctly labelled Stem-and-Leaf Display c. Draw /Construct a correctly labelled Pie Chart Answers: A.i. The population of interest in the given question is the total number of registered voters in the city i.e. 55,000.ii. The sample in the given case is the number of people chosen from the population to be interviewed i.e. 250.iii. 52% is a statistic and not a parameter since it describes about the characteristic of the sample and not the population. This is apparent since the given information clearly states that 52% of those interviewed (i.e. sample of 250) would vote.B.i. The parameter in the given case is not calculated since parameter is derived from the population i.e. all the students at the Eastern Suburbs Community College but the research confines to only a sample of 350 students.ii. The statistic in the given case is 15.5 km since it summaries the information based on the sample of 350 students at the Eastern Suburbs Community College.iii. The population in the given case would constitute all those students who are commuting and studying at the Eastern Suburbs Community College. However this figure is not given in the given case.2. A. Nominal data are commonly use to depict data which cannot be quantified and thus primarily requires labelling such as sex, marital status etc.Ordinal data is normally used to denote different degrees or orders of a particular value where the exact difference between the various degrees cannot be exactly quantified. For instance, the level of satisfaction can be low, moderate or high but the exact difference between these three cannot be accurately quantified or defined.Interval data is used to denote those numeric values where the various degrees are known and additionally the exact difference between the various degrees can also be exactly quantified. For instance the values on a speedometer can be classified as interval data.B.i. Data type is Ordinal since the given data since the exact difference is not known.ii. Data type is interval since the reading of the odometer can be easily quantified in the form of interv als.iii.Data type is nominal since the data cannot be quantified and would primarily involve the use of labels such married, unmarried and divorced.iv. Data type is ordinal since the given data measures the degree of satisfaction where the difference between various satisfaction degrees cannot be exactly quantified.v. Data type is interval since the result in % is quantifiable and thus can be grouped into intervals.vi. Data type is interval since the given data primarily presents labels represent the performance of the student which can be quantified as the pass , fail depend on particular range of marks.3. i. The histogram for the given data is shown below. 1. The stem leaf plot is as shown below. Stem Leaf 0 3,9 1 2,3,3,3,4,4,4,5,6,7,8,8,8,8,8,8,8,9,9 2 0,0,0,2,3,3,3,4,4,4,4,5,5,5,6,6,6,7,8,8,8,8,8,9,9,9,9 3 0,0,0,0,0,1,1,5,6,6,6 4 2 iii. The relative frequency table of the given data is shown below. Value Frequency Relative Frequency 0 to 5 1 1.67% 5 to 10 1 1.67% 10 to 15 7 11.67% 15 to 20 12 20.00% 20 to 25 11 18.33% 25 to 30 16 26.67% 30 to 35 7 11.67% 35 to 40 4 6.67% 40 to 45 1 1.67% Total 60 100.00% The pie chart corresponding to the above is shown below.