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Statistics Final Descriptive Statistics and Graphs 1. Reproduce the data set from a stemplot or vise versa (continuous or discrete data) Descriptive Statistics-organizing and summarizing informationInferential Statistics-Drawing conclusions about a population based on data collected from a sample of the population Qualitiative Variable- responses to questions like “what kind of advertising do you use”; yes or no questions Maybe a # like a zip code/area code but cant do calculations;Quantitative Variables-things that can be counted or measured, data that can be added, multiplied(ratings, weight, time, temp)-Mathematical operations. Can be either continuous or discrete. Continuous data-a # with a decimal Discrete Data- A quantitative variable whose possible values can be listed. A quantitative variable with only a finite #of possible values is a discrete value Frequency-# of times a particular distinct value occurs. -A frequency distribution provides a table of the values of the observations and how often they occur. To construct a Frequency Distribution of Qualitative data Step 1- list the distinct values of the observations in the data set in the first column of a table Step 2-For each observation, place a tally mark in the second column of the table in the row of the appropriate distinct value. Step 3: Count the tallies for each distinct value and record the totals in the third column of the table Step 4: interpret Relative Frequency distributions Relative Frequency- is the ratio of the frequency to the total #of observations, it provides a table of the values of the observations and(relatively) how often they occur: Relative Frequency=frequency# ofobservationsRelative Frequency Distribution of Qualitative Data-is a listing of the distinct values and their relative frequencies. To constuct a Relative-Frequency Distribution of Qualitative Data Step 1: obtain a frequency distribution of the data Step 2: Divide each frequency by the total # of observations Step 3: Interpret -Relative-Frequency distributions are better than frequency distributions for comparing 2 data sets, bc relative frequencies always fall between 0 and 1, they provide a standard for comparison.
Two common methods of displaying qualitative data are pie charts and bar charts. Pie Charts- a disk divided into wedge-shaped pieces proportional to the relative frequencies of the data.
To Construct a pie Chart Step 1: Obtain a relative-frequency distribution of the data Step 2: Divide a disk into wedge shaped pieces proportional to the relative frequencies Step 3: Label the slices with the distinct values and their relative frequencies
Bar chart- graphical display for qualitative data. Frequencies, relative-frequencies, or percents can be used to label a bar chart. Displays distinct values of qualitative data on a horizontal axis and the relative frequencies on the vertical axis. The relative frequency is represented by a vertical bar whose height is equal to the relative frequency of that value. The bars should not touch each other. To construct a bar chart; Step1: obtain a relative frequency distribution of the data Step2: Draw a horizontal axis on which to place the bars and a vertical axis on which to display the relative frequencies Step 3: For each distinct value, construct a vertical bar whose height equals the relative frequency of that value. Step 4: Label the bars with the distinct values, the horizontal axis with the same of the variable, and the vertical axis with “Relative Frequency”
Organizing Quantitative Data: We first group observations into classes(categories, bins) then treat the classes as the distinct values of qualitative data. Once we group the quantitative data into classes, we can construct frequency and relative-frequency distributions of the data the exact same way we did for qualitative data. Important guidlines for grouping quantitative data into classes: 1. # of classes should be small enough to provide an effictive summary but large enough to display the relevant characteristics of the data. A rule of thumb is that the # of classes should be between 5 and 20. 2. Each observation should belong to one, and only one, class. Meaning, each observation must belong to one class. 3. If possible every class should cover the same # of possible values. These guidlines provide a solid basis for grouping data. group quantitative data into classes we use 3 common methods: single-value grouping, limit grouping, and cutpoint grouping Single value grouping-represents a single possible value, use with discrete data in which there are only a small #of distinct values. Limit grouping- uses class limits. Each class consists of a range of values. Smallest value that could go in a class is called the lower limit, lagest value that could go in the class is call the the upper limit of the class. Use when the data are expressed as whole #’s and there are too many distinct values to use single-value grouping. Class width difference between the lower limit of a
class and the lower limit of the next-higher class. Class mark the average of the two class limits of a class. Cutpoint grouping-consists of a range of values. Smallest value that could go in a class is called the lower cutpoint, and the smallest value that could go in the next higher class is called the uppercutpoint of the class. The lower cutpoint is the same as its lower limit and that the upper cutpoint of a class is the same as the lower limit of the next higher class. Class width the difference between the cutpoints of a class. Class midpoint the average of the two cutpoints of a class. Use when the data are continuous and are expressed with decimals. Three common ways of displaying quantitative data are histograms, dotplots, and stem-and-leaf diagrams. Bin width formula=# ofbinsmax−minHistograms- provides a graph of the values of the observations and how often they occur. It displays the classes of the quantitative data on a horizontal axis and the frequencies(relative frequency, percent) of those classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency of that class. The bars touch eachother. For single value grouping we use the distinct values of the observations to label the bars, each value should be centered under the bar. For Limit or cutpoint grouping we use the lower class limits(or cutpoints) to label the bars. When the frequencies are on the vertical axis this is a frequency histogram. To construct a Histogram: Step 1: Obtain a frequency distribution of the data Step2: Draw a horizontal axis on which to place the bars and a vertical axis on which to display the frequencies(relative-frequencies, percents) Step 3:For each class, construct a vertical bar whose height equals the frequency of that class Step 4: Label the bars with the classes, the horizontal axis with the name of the variable, and the vertical axis with “frequency”(“relative frequency”, “percent”). -Relative-Frequency or percent histograms are better than frequency histograms for comparing two data sets. The same vertical scale is used for all relative frequenct histograms--min 0 and a max of 1--making direct comparison easy. The vertical scale of a frequency histogram depends on the # of observations, making comparison more difficult.
Stem-and-leaf Diagram- In a stem and leaf diagram or a stemplot each observation is seperated into two parts 1. Stem- consisting of all but the rightmost digit and 2. Leaf- the righmost digit. Stems may use as many digits as required, but each leaf must contain only one digit. To Construct a Stem-and-Leaf Diagram: Step 1: Think of each observation as a stem-consisting of all but the rightmost digit-and a leaf, the rightmost digit. Step 2: Write the stems from smallest to largest in a vertical column to the left of a vertical rule Step 3: Write Each leaf to the right of the vertical rule in the row that contains the appropriate stem.
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School: Auburn University
Course: Statistics for Health Sciences
Professor: Regina Halpert
Term: Fall 2015
Name: THE DMS 2510 - Statistics for Health Sciences - Study Guide - Descriptive Statistics and Graphs
Description: Statistics Final Descriptive Statistics and Graphs 1