DSCI 2710 1st EditionExam # 1 Study Guide Lectures: 1 - 5Lecture 1 Population vs. SamplePopulation (size is N)Ex: all students at UNT- All students that own a car- All registered voters- All production workers at Motorolao You measure or count something for each of these. That is the population.Sample (size is n)Usually selected randomly- Called a simple random sample- Random samples provide a better representation of the populationDescriptive & Inferential StatisticsDescriptive Statistics: use descriptions to group statsInferential Statistics: take data and make inferences*Prescriptive: tell you what to doSample DataCan be discrete or continuous - Discrete: when you’re counting something- Continuous: when you’re measuring somethingo Level of Measurement “weak” data vs. “strong” data Weakest- Nominal (a category or label)- Ordinal (ranks)- Interval (differences are meaningful) Strongest- Ratio (the word twice makes sense)Nominal vs. Interval DataNominal data are the weakest data and represent a category- Ex: gender, ethnicity, hair color- Only discuss proportions here o Ex: In a sample population we night find that 58% of the people are female and 42% maleInterval Data Difference between values is meaningful- i.e. temperatureLecture 2 Frequency Distribution(How to Construct)1. Gather sample data2. Arrange in an ordered array3. Select the number of classes to be used4. Determine class width5. Determine class limits for each class6. Count the number of data values in each class (the class frequencies)7. Summarize the class frequencies in a frequency distribution tableWhen looking at data:H(highest) – L(lowest)KLecture 3Descriptive graphsbell curven= sampleN= population Measures of Central Tendency- Determine the center of your data values or possibly the most typical data value- Variation: will not always be a normal curve- Position: will not always be in the same spot, can be skewedMeanH(highest) – L(lowest)- The average numberData: 5,6,7,9,23(5+6+7 +7+23)/5 = 10 x= (Σ xἰ) nMedian- Middle number (50th percentile)- Md= (n+1)/2Mode- m₀= most frequent observationMidrangemr= (L+H)/ 2RangeR= H (highest) – L (lowest)Standard DeviationStd. Dev. = √variations²=(Σx²- ∑ x²/n)/n-1variance = sLecture 4Current LectureDescriptive MeasuresZ scorez = x – xsx, s= sampleµ,δ= populationLecture 5Current LectureTime Series – the value of a given variable (such as your natural gas usage per month or the costof college tuition per year) usually measured at equal intervals of time such as years, quarters, months, weeks or days – i.e. the value of that variable at a given point in time.Trend (TR) - the long term increase or decrease in a time series 0 (+) (-) zMd x (+) And the (-) goes the opposite way.Seasonality (S) – the increase and decreases that occur in the variable within a calendar year (like the sales of snowmobiles in winter vs. summer or the consumption of soft drinks in summer vs. winter.) You cannot have seasonality or at least cannot analyze for seasonality if you only have annual data – you must have data that in less than annual to analyze for seasonality.Cyclical (C) – the long term movement of the variable about the trend; usually attributed to business and economic cycles (like the boom of the late 90’s and the downturn from late 2000 in till today).Irregular Activity (I) – essentially what we cannot explain by the above three – TR, S, & C. often includes unpredictable events in time – strikes, wars, earthquakes, hurricanes etc.We combine these elements in a multiplicative model (which means we multiply the factors noted above) to explain the value of a variable y at point t in time.The full multiplicative mode including seasonality is yt= (TRt)(St)(Ct)(It)Note if we only annual data then Model is yt= (TRt)(Ct)(It) because it has no