HP340: Statistical Methods, Spring 2015Due Date: January 27, 20151. Define and give two examples (each) of:a. A continuous variableA continuous variable can take on any value between the maximum and minimum value. One example is time, time can take on any hour variable between 1 and 12. Another example is air pressure because the value could have increasing amounts of decimal places.b. A discrete variableA discrete variable is one that can take on a certain amount of values. An example is a population of animals because you can only have 72 or 73 animals, not 72.5. Another example is the outcome of a soccer game because nobody can score half a point it has to be a whole number.2. For nominal, ordinal, interval and ratio measurements, indicate which of the following can be calculated:3. Describe the following variables qualitatively, quantitatively and categorically(i.e. as an ordinal variable):a. Income per yearQualitatively: high income versus low incomeQuantitatively: income measured in dollarsCategorically: below average income, average income and above average incomeb. Population densityQualitative: high density versus low densityQuantitative: density measured in number of people in a certain area of land.Categorical: population in an urban area and population in a rural area.Measurement typeCan youcalculate?Nominal Ordinal Interval RatioFrequencydistributionyes yes yes yesPercentiles no yes yes yesAddition orsubtractionno no yes yesMedian no yes yes yesMean no yes yesStandarddeviationno no no yesc. Systolic blood pressureQualitative: high systolic blood pressure, low systolic blood pressureQuantitative: 110 bpm, 120 bpmCategorical: normal, pre-hypertension, stage 1 hypertension, stage 2 hypertension.4. To study the mood of first-year USC undergraduate students during exams week, 25 first-year students were interviewed and their mood recorded, using a mood scale that ranges from 5 (bad mood) to 30 (excellent mood).a. Describe the sample and population of this study.The sample is a random group 25 first-year undergraduates. The population is USC undergraduates.b. Using the raw data provided in the Excel spreadsheet (HW1 Data.xls), construct a frequency table similar to what was shown in class (and table 3.2). Specify the score, frequency, relative frequency, percent frequency.Score TallyFrequencyRelativefrequency (rf)Percentfrequency(%f)CumulativefrequencyCumulative relativefrequencyCumulativepercentagefrequency30 0 0.00 0%25 1 100%29 0 0.00 0%25 1 100%28 0 0.00 0%25 1 100%27 0 0.00 0%25 1 100%26 0 0.00 0%25 1 100%25 / 1 0.04 4%25 1 100%24 / 1 0.04 4%24 0.96 96%23 /// 3 0.12 12%23 0.92 92%22 / 1 0.04 4%20 0.8 80%21 0 0.00 0%19 0.76 76%20 /// 3 0.12 12%19 0.76 76%19 // 2 0.08 8%16 0.64 64%18 / 1 0.04 4%14 0.56 56%17 / 1 0.04 4%13 0.52 52%16 0 0.00 0%12 0.48 48%15 / 1 0.04 4%12 0.48 48%14 0 0.00 0%11 0.44 44%13 // 2 0.08 8%11 0.44 44%12 /// 3 0.12 12%9 0.36 36%11 / 1 0.04 4%6 0.24 24%10 0 0.00 0%5 0.2 20%9 / 1 0.04 4%5 0.2 20%8 0 0.00 0%4 0.16 16%7 0 0.00 0%4 0.16 16%6 // 2 0.08 0%4 0.16 16%5 // 2 0.08 8%2 0.08 8%c. What are the lowest and highest scores obtained?The lowest score obtained was 5 and the highest was 25.d. What is the most frequently occurring score?The most frequently occurring scores are 23,20 and 12e. Add three more columns to your frequency table and calculate the cumulative frequency, cumulative relative frequency, and cumulative percentage frequency. (look at B)5. This question is adapted from K&G “Testing Your Knowledge 3.2” question. Inconducting this study, researchers recorded 50 observations of gazelle – predator distances in meters. These raw data are in HW1 Data.xls (second worksheet tab). a. Using the raw data scores, construct a table of the grouped distributions, including: frequency, relative frequency, percentage frequency, cumulative frequency, cumulative relative frequency, and cumulative percentage frequency. Use 20 class intervals.Distance Tally FrequencyRelative frequency (rf)Percent frequency (%f)Cumulative frequencyCumulative relative frequencyCumulative percentage frequency18-26 // 2 0.04 4%2 0.04 4%27-35 /// 3 0.06 6%5 0.10 10%36-44 /////// 7 0.14 14%12 0.24 24%45-53 ///////// 5 0.10 10%17 0.34 34%54-62 ////////// 10 0.20 20%27 0.54 54%63-71 ///////// 9 0.18 18%36 0.72 72%72-80 /// 5 0.10 10%41 0.82 82%81-89 /// 3 0.06 6%44 0.88 88%90-98 // 2 0.04 4%46 0.92 92%99-107 0 0.00 0%46 0.92 92%108-116 0 0.00 0%46 0.92 92%117-125 0 0.00 0%46 0.92 92%126-134 0 0.00 0%46 0.92 92%135-143 / 1 0.02 2%47 0.94 94%144-152 0 0.00 0%47 0.94 94%153-161 / 1 0.02 2%48 0.96 96%162-170 0 0.00 0%48 0.96 96%171-179 0 0.00 0%48 0.96 96%180-188 0 0.00 0%48 0.96 96%189-197 / 1 0.02 2%49 0.98 98%198-20 / 1 0.02 2% 50 1.00 100%b. Describe what you see in this group frequency table, and draw conclusions on what these data indicate about gazelle-predator distances.The gazelle-predator distance in concentrated within the first 100 meters. The mode is in between 54 and 62 meters.c. Find the percentile rank of a distance of 68 meters.76%d. What are the 25 th , 50 th and 75 th percentiles of this distribution?25th= 4450th= 5375th= 71e. Construct a histogram and a frequency polygon for the distances usingthe (simple) frequencies of the grouped distribution with a class interval of 10 meters.(see