Statistics final wgu academy with complete questions and answers

Statistics final wgu academy with complete questions and answers nominal variables - Categorical variables that there is no natural order among the categories ordinal variable - Categorical variables where there is natural order among the categories (low-high) interval - A measurement which makes sense to talk about the difference between values but not the ratio between values ratio - Quantitive variables where is makes sense to talk about the difference in ratios. (Income, weight) In ratios: - Value 0 means the absence of quantity (income $0) Distribution of a Variable - Tells us what values the variables take and how often they take those values In intervals: - Vale 0 does not mean the absence of value (temp = 0F) Pie charts - Emphasize how the different categories relate to the whole Bar charts - Emphasize how the different categories compare with each other Histogram - Breaking the range of values into intervals and count how many observations fall into interval. Stemplot(stem and leaf plot) - Graphical display of quantitive data. Data is spread into "stem" and "leaf". It retains the data and sorts. Boxplot - Graphically represents the distribution of a quantitive variable. Visually displays the five number summary and the observations classified as a suspected outlier. Measures of Center - Mode, mean, and median. Mode - The most commonly occurring value. Can be unimodal or bimodal Mean - The average of a set of observations. The sum of observations divided by the number of observations. (x bar) Median - The midpoint of the distribution. (M) Measures of soread - Range, inter quartile range (IQR), standard deviation How to find the median - -order the data smallest to largest -if the number(n) of observations is odd (n+1)/2nd spot -if the number(n) of observations is even we have two n/2 = spot & n/2 + 1 = spot Measure of center that is sensitive to outliers - Mean Measure of center that is not sensitive to outliers - Median Symmetric distributions - Mean and median will be approximately equal skewed right - Mean will be greater than the median skewed left - Mean will be less than the median range - The exact distance between the smallest data point and the largest. The most intuitive measure of variability. Inter-Quartile Range (IQR) - Measures the variability of a distribution by giving us the range covered by the MIDDLE 50% of the data. - Step 1: Arrange the data in increasing order, and find the median - Step 2: Find the median of the lower 50% of the data = 1st quartile (Q1) - Step 3: Repeat this again for the top 50% of the data = 3rd quartile (Q3) - Step 4: The middle 50% of the data falls between Q1 and Q3. Therefore: IQR = Q3 - Q1 Note: When finding the median of an odd number of data items, it is not included in either the bottom or top half of the data; when median is even, the data are naturally divided into two halves. When should the IQR be used? - Only when the median is used as a measure of center. When should an outlier be kept in the data? - -when the outlier is produced by the same sort of physical or biological process as the rest of the data. -the outlier is expected to eventually occur again five number summary - min, Q1, median, Q3, max standard deviation - Quantifies the spread of a distribution by measuring how far the observations are from their mean. ( gives the average distance between a data point and the mean (xbar) how to find standard deviation? - -find the mean -find deviations from the mean (xbar - 2,3,4,5 etc) -square each deviation -add all squared deviations then divide them by n - 1 (sample size minus 1) -find square root of new total, this is the standard deviation Variance of data - The average of the squared deviations When to use x-bar and SD as numerical summary? - Only for reasonably symmetric distributions with no outliers When to use the median and IQR as a summary? - All other cases that are not symmetric How many observations fall within 1 SD of the mean? (Normal distribution) - 68% How many observations fall within 2 SD of the mean? (Normal distribution) - 95% How many observations fall within 3 SD of the mean? (Normal distribution) - 99.7% explanatory variable - Also called the independent variable. The variable that claims to explain, predict, or affect the response. Denoted by X. response variable - Also known as the dependent. The outcome of the study. Denoted by Y. Case C - Q - -data displayed with side by side box plots -numerical summaries: descriptive statistics Case C - C - Use two way table to simplify and summarize data. Use conditional percentages in two way table. Find conditional percentages by dividing the cell number by total. Case Q - Q - Use a scatterplot Where should the explanatory variable be placed? and the response? - The explanatory should always be put on the horizontal X-axis. The response should always be on the vertical Y-axis. Correlation Coefficient r - The numerical measure used to asses the strength of a linear relationship. What are the four points of correlation coefficient r? - -The value of r ranges from -1 - 1 -Values of r that are close to 0 either positive or negative indicate a weak relationship. -Values close to -1 or 1 indicate a strong relationship -r is unit-less. Changing the type of units the response variable will not change the r.