Clemsonaphistudy.weebly.com



Chapter 3 – Organizing, Displaying, and Interpreting DataFrom information about baseball to information about income, the most basic task when working with data is to summarize a great deal of information. Graphical images are universally regarded as a powerful method of communicating data. We will use the following to graphically display data:Graphical Displays for Qualitative DataFrequency/Relative Frequency DistributionBar ChartStacked Bar ChartPie ChartGraphical Displays for Quantitative DataFrequency/Relative Frequency DistributionHistogramStem and Leaf DisplayDot PlotsTime Series DataQualitative Data - Frequency Distributions Data organization using a table:A frequency distribution summarizes data by category (class) and the number of observations of each category.A relative frequency distribution summarizes data by category and the relative frequency or the proportion of observations in each category.You should be able to create frequency distributions with and without the use of technology. Example 1: Olympic HockeyThe table shows the gold medal winners in hockey in the Winter Olympics since 1920. Complete the table below to create a frequency and relative frequency distribution. Source: YearWinnerYearWinnerYearWinner1920Canada1960U.S.A.1992Unified Team1924Canada1964Soviet Union1994Sweden1928Canada1968Soviet Union1998Czech Republic1932Canada1972Soviet Union2002Canada1936Great Britain1976Soviet Union2006Sweden1948Canada1980U.S.A.2010Canada1952Canada1984Soviet Union2014Canada1956Soviet Union1988Soviet Union Frequency Distribution Relative Frequency DistributionWinnerFrequencyCanada9Soviet Union7U.S.A.2Great Britain1Sweden2Czech Republic1Unified Team1WinnerRelative FrequencyCanada9/23Soviet Union7/23U.S.A.2/23Great Britain1/23Sweden2/23Czech Republic1/23Unified Team1/23 TOTAL: 23TOTAL: 23/23With large data sets, it is useful to be able to create a frequency and relative frequency distribution using technology. Instructions for creating these using Excel and Minitab may be found in the Chapter 3 Technology Guide.Qualitative Data – Bar Charts and Pie ChartsA bar chart displays the categories and a bar representing the frequency or relative frequency of each category.Bar Chart with FrequenciesBar Chart with Relative FrequenciesPie ChartA pie chart provides the relative frequencies of each category represented by the proportion of a circle that corresponds to the relative frequency.Qualitative Data - Stacked Bar ChartsWhile a bar chart represents the frequencies of categories of one variable, a stacked (segmented) bar chart represents the frequencies of combinations of categories of two variables.Example 2The following stacked bar graph represents the medal count results for the top ten countries (by total medal count) in the 2014 Winter Olympics in Sochi.Example 2: Interpreting a Stacked Bar GraphUse the graph above to answer the following.a. How many bronze medals did Canada earn?5b. What proportion of medals earned by Canada were bronze?5/25c. Which country earned the most bronze medals?U.S.A. Example 3:Consider the sales performance of the following sales persons.SalespersonTotal Sales (Thousands of Dollars)Susan187William201Beth207Rob193-13271527178000The first bar chart more accurately depicts the roughly 10% difference in sales performance.Using Excel, create a stacked bar graph with the following data representing the overall medal counts from the 2016 Rio Olympics.COUNTRYGOLDSILVERBRONZETOTAL?USA463738121?GBR27231767?CHN26182670?RUS19181956?GER17101542?JPN1282141?FRA10181442?KOR93921?ITA812828?AUS8111029Quantitative Data - Frequency and Relative Frequency DistributionsWhen data are qualitative, selecting the categories for display is relatively easy. When the data are quantitative, this is not particularly obvious. One should consider the range of values in the dataset along with the number of categories (bins) desired when constructing a frequency or relative frequency distribution. Be sure that number of categories and bin width appropriately represents the data set. Example 1: Poverty Level by StateThe following table gives the percent of people living below the poverty level for each state and the District of Columbia in the year 2015. Percent of People Living Below the Poverty Level by State18.510.515.119.622.010.816.116.717.910.312.413.613.414.820.415.415.912.117.417.314.59.714.615.413.211.311.119.115.712.211.512.616.413.910.215.317.013.015.814.711.016.611.211.510.618.510.28.214.813.712.2The data ranges from roughly 8% to roughly 22% so a bin width of 2% seems reasonable.We may summarize these data using a frequency distribution, relative frequency distribution and cumulative relative frequency distribution.Source: 2015 American Community SurveyPercent of People Living Below the Poverty LevelFrequency(Number of States)Relative Frequency of )Cumulative Relative Frequency[8.2 , 10.2]44/514/51(10.2 , 12.2]1313/5117/51(12.2 , 14.2]88/5125/51(14.2 , 16.2]1313/5138/51(16.2 , 18.2]77/5145/51(18.2 , 20.2]44/5149/51(20.2 , 22.2]22/5151/51Example 2: Using the Cumulative Relative Frequency DistributionUse the table that you created in Example 1 to answer the following.A. What proportion of states have less than or equal to 16.2% of the population living below the poverty level?0.74B. What proportion of states have more than 14.2% of the population living below the poverty level?1-.49=.51The frequency tables that you created in the previous example may be displayed graphically using a histogram.A histogram is a graph that uses bars to portray the frequencies or relative frequencies of the possible outcomes of the variable. It is a useful graphical tool for large quantitative data sets. Quantitative Data – Stem and Leaf DiagramsAnother useful tool for displaying data is a stem and leaf diagram. The stem and leaf diagram is similar to a histogram however, unlike a histogram, the values of the original data set are apparent given the display.A stem and leaf diagram may be constructed using the following steps:Step 1: Sort the data from low to highStep 2: Split the values into stem and leaf:leaf = units place: stem = all digits left of the units placeFor example, for the value 112, the stem is 11 and the leaf is 2.Step 3: List the stems from lowest to highestStep 4: Order the leaves from lowest to highest and place next to each stem.Example 3: Days to PaymentThe following data represent the number of days required to collect insurance payments for a random sample of customers of a local dentist.Number of Days to Collect Payment345536393632353047316066484333243738653522453329413835285656Create a stem and leaf display for these data.Qualitative Data – Dot PlotsA dot plot shows a dot for each observation, placed above each value on the number line for that observation. Like the stem and leaf plot, it portrays each observation (you can recreate the data set from the plot). The following shows a dot plot for a distribution of test scores.The Shape of a Distribution?The shape of a distribution is described by mentioning any symmetry or skewness, the number of peaks, any clusters or gaps, and any unusually high or low observations, called outliers.??In describing the shape of a distribution, concentrate on the main features. ─Look for rough symmetry or clear skewness. ─Look for major peaks or gaps, not just for minor ups and downs in the bars of the histogram. ─Look for clear outliers not just for the smallest and largest observations.2040890000?In determining the shape of a distribution, it is often helpful to outline a graph with a smooth curve.?Symmetry vs. skewness:─A distribution is symmetric if the right and left sides of the graph are approximate mirror images.─A distribution is skewed left if the left side of the graph extends much further out than the right.─A distribution is skewed right if the right side of the graph extends much further out than the left.Describing The Shape of a DistributionA way to remember how to describe a distribution?Center? (mean, median)?Unusual (any outliers)?Shape (symmetric- be careful!, skewed, uniform, bimodal)?Spread (range, interquartile range, standard deviation)Example 4Describe the shape of the fat content in McDonald’s breakfast menu items, based on the stem-and-leaf plot. Key 1|3 = 13 grams.2839720571500Skewed right with a gap in the 40’s and one unusually high observation of 56g.0Skewed right with a gap in the 40’s and one unusually high observation of paring Two Distributions?When you are asked to compare two distributions, you need to discuss the similarities and/or differences in their shapes, their centers, and their spreads.─Provide a measure of center for each distribution, and discuss which one is larger/smaller. (Chapter 4)─Provide a measure of spread for each distribution, and discuss which is larger/smaller. (Chapter 4) Example 5These dot plots represent pet ownership in two different city blocks. Write a sentence to compare their shape.-2457455080003069590116840It appears that block A is right skewed while block B is more symmetric and mound shaped.It appears that block A is right skewed while block B is more symmetric and mound shaped. Chapter 3 PracticeObesity, high blood pressure, high cholesterol, and heart disease are partially caused by a poor diet. As such, the FDA requires nutrition labels on most packaged foods. Below is a dot plot of the amount of sugar contained in a single serving of 12 popular breakfast cereals.Describe the shape of the distribution.The distribution is approximately symmetric and bimodal with a gap from 5 to 10 grams of sugar.The following histogram represents data for the percentage of people without health insurance for the 50 states in 2013. ?How would you describe the shape of the distribution of uninsured rates for the 50 states from the histogram below?Approximately symmetric & unimodalSuppose we survey everyone in the STAT 3090 and ask them what month they were born in (January, February, etc.). Which of the following graphs would be most appropriate for displaying the results?Bar GraphHistogramBar GraphWhat is the difference between a frequency distribution and a relative frequency distribution?A frequency distribution summarizes data by category (class) and the number of observations of each category whereas a relative frequency distribution summarizes data by category using the proportion of observations in each category.A survey asked students to report the web browser they primarily use. The relative frequency bar graph below summarizes the 639 student responses. ?How many more respondents primarily use Chrome than primarily use Firefox?About 345 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download