Introductory Statistics Exam Questions with Verified Answers Rated A+ (Already Passed)

Introductory Statistics Exam Questions with Verified Answers Rated A+ (Already Passed) Descriptive statistics - Answers refers to numerical facts such as averages, medians, percents, and index numbers that help us understand the reality via available data. Data - Answers are facts and figures collected, analysed and summarized for presentation and interpretation data set - Answers is a collection of all data in a particular study elements - Answers are the entities on which data are collected variable - Answers is a characteristic of interest for the elements measurements - Answers on each variable for every element in the study provide data set observation - Answers is the set of measurements for a particular element Nominal scale - Answers data for a variable consist of labels or names used to identify an attribute of the element. For numerical purposes may be replaced by a numerical code 1, 2, . . . . E.g. Fund type, sex, nationality. Ordinal scale - Answers data exhibit the properties of nominal data and the order or rank of the data is meaningful. Ordinal data can also be provided using a numerical code. E.g. Morningstar Rank, highest achieved education Interval scale - Answers data have all the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Interval data are always numerical. E.g. year of birth, temperature in degrees Celsius. Ratio scale - Answers data have all the properties of interval data and the ratio of two values is meaningful. This scale requires that zero value be included. The scale of most of the variables we measure is a ratio scale. E.g. cost of a car, time, weight, distance. Categorical data - Answers data grouped by specific categories; of either nominal or ordinal scale of measurement. Sometimes referred to as qualitative data. Statistical analysis of categorical variables is limited, we can summarize by counting number or proportion of observations in categories. It may not have sense to consider characteristics such as sum or average. Quantitative data - Answers data with numerical values indicating "how much" or "how many". Arithmetic operations provide meaningful results for qualitative variables. Cross - Answers sectional data - collected at the same or approximately the same point of time. E.g. Morningstar data set time Series data - Answers collected over several time periods. E.g. average price per gallon of gasoline between 2006 to 2009. experimental study - Answers a variable of interest is identified first. Then one or more other variables are identified and controlled so that data can be obtained about how they influence the variable of interest. E.g. effects of a new drug on blood pressure. Observational or non - Answers experimental studies - make no attempt to control the variables of interest. E.g. survey, when research questions are first identified and a questionnaire is designed and administered to a sample of individuals Population - Answers large group of elements, set of all elements of interest in a particular study (e.g. voters, companies, products etc.) but because of some reason (time, cost, etc.) data are collected from only a small portion of a group - sample - a subset of population Census - Answers Conducting a survey to collect data for the entire population Sample survey - Answers collecting data for a sample census - Answers is the procedure of systematically acquiring and recording information about the members of a given population Statistics uses data from a sample to make estimates or test hypotheses about the characteristics of a population through a - Answers statistical inference Statistical inference - Answers is the process of deducing properties of an underlying distribution by analysis of data. Frequency distribution CD - Answers is a tabular summary of data showing the number of each items in each of several non-overlapping classes Relative frequency CD - Answers of a class equals the proportion of items belonging to a class Percent frequency CD - Answers of a class is the relative frequency expressed in percents (multiplied by 100) Relative (percent) frequency distribution CD - Answers gives a tabular summary of relative (percent) frequency for each class Bar chart CD - Answers is a graphical representation of categorical data summarized in a frequency, relative frequency or percent frequency distribution; the bars should be separated to emphasize that each class is separate. Pie chart CD - Answers provides another such graphical device Frequency distributions QD - Answers as for categorical data; one has to define the non-overlapping classes Number of classes QD - Answers depending on size of the data set; use enough classes to show the variation in the data; general guideline to use 5-20 classes Width of the classes QD - Answers usually same for each class; approximate width as range of data divided by number of classes rounded to a convenient value Class limits QD - Answers chosen such that each data item belongs to a unique class Class midpoint QD - Answers useful in some applications; value halfway between the lower and upper class limit Dot plot QD - Answers is the simplest graphical summary Histogram QD - Answers is a common graphical presentation of quantitative data summarized in some frequency distribution; spaces between classes are eliminated to show that all values in the range of data are possible stem - Answers and-leaf display QD - is a technique of exploratory data analysis to show both shape and rank order of a data set crosstabulation or contingency table - Answers is a tabular summary of data for two variables. Left and top margin labels define the classes for the two variables. Each observation is associated with a cell. Useful for inspecting the strength or symmetry of the relationship between the two variables the data in two or more crosstabulations are often combined or aggregated. Conclusions based on unaggregated data can be reversed - Answers Simpson's paradox Scatter diagram or scatter plot - Answers is a graphical representation of the relationship between two quantitative variables Trendline or regression line - Answers is the line that provides an approximation of the relationship Sample statistics - Answers are numerical summary measures computed for data from a sample Sample mean - Answers or average value provides a measure of central location for the data In some applications each observation has its own weight reflecting its importance and we compute - Answers weighted sample mean (sample) median - Answers is another measure of central location, remains unchanged (robust) Mode - Answers is the value that occurs with greatest frequency Sample quantile or percentile - Answers provides information about how the data are spread over the interval from the smallest value to the largest value First quartile or lower quartile - Answers Q1 is the 25th percentile. Second quartile - Answers is the median, i.e. the 50th percentile, sometimes denoted as Q2. Third quartile - Answers or upper quartile Q3 is the 75th percentile Measures of variability - Answers provide information about dispersion of values of data in the data set Range - Answers is the difference between the largest and the smallest value; rarely used as it depends on two extreme values only Interquantile range (IQR) - Answers is the difference between upper and lower quartiles, Q3 − Q1, i.e. the range for the middle 50% of the data. Sample variance - Answers is the average square distance from the mean It is expressed in units squared, thus its positive square root is often considered - Answers sample standard deviation SD - Answers the standard deviation is commonly used measure of the risk associated with investing in stock and stock funds. It provides measure of how monthly returns fluctuate around the long-run average return z-score - Answers is a measure of relative location of values within a data set; how far a particular value is from the mean in terms of standard deviation as a unit ZS - Answers Sometimes called standardized value; positive (negative) z-scores indicate values larger (smaller) than mean. A z-score of zero indicates that the observation is equal to the sample mean. outliers - Answers data with unusual small or large values with respect to the data set. Can be an incorrectly recorded value or an observation incorrectly included in the data set (can be corrected or removed after careful inspection). Or it is just a correct value of an unusual observation that belongs to the data set. Empirical rule: outlier - outlier is an observation with z - Answers score less than -3 or greater than 3. five - Answers number summary - we specify the following five values to summarize the data: smallest value, lower quartile, median, upper quartile, maximum value Box plot - Answers is a graphical summary based on five-number summary. Interquantile range and outliers are also used.