IT-DescribingQuantitativeData-Histograms.ppt

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1、Describing Quantitative Data-HistogramsRecall that quantitative data measures a Recall that quantitative data measures a characteristic.characteristic.These measurements may result in a few distinct These measurements may result in a few distinct values(number of siblings)or in many distinct values(

2、number of siblings)or in many distinct values(commute times).values(commute times).We will focus on quantitative data which has too We will focus on quantitative data which has too many distinct values to allow each number to be its many distinct values to allow each number to be its own group.We wi

3、ll define intervals which may own group.We will define intervals which may contain different values.contain different values.Describing Quantitative Data-HistogramsWe will make a graph that is similar to a bar graph We will make a graph that is similar to a bar graph called a histogram.If we did thi

4、s by hand our steps called a histogram.If we did this by hand our steps would be:would be:l define the intervals(determine a width)define the intervals(determine a width)l list the intervals and the number of data values in list the intervals and the number of data values in each interval in a table

5、 each interval in a tablel draw the histogram draw the histogram Each interval will have the same width.Each interval will have the same width.The frequency(or relative frequency as a percent)The frequency(or relative frequency as a percent)will determine the height of the rectangle.will determine t

6、he height of the rectangle.Describing Quantitative Data-HistogramsThe histogram will look like a bar chart,but the The histogram will look like a bar chart,but the intervals will be right next to each other.There may intervals will be right next to each other.There may not be spaces between bars.not

7、 be spaces between bars.Note:Spaces would actually be intervals with no Note:Spaces would actually be intervals with no observations,so technically,there is never space observations,so technically,there is never space between bars in a histogram.between bars in a histogram.We will use Minitab to pro

8、duce histograms,so we We will use Minitab to produce histograms,so we will focus on interpreting the picture,rather than will focus on interpreting the picture,rather than producing it by hand.producing it by hand.Histogram Example#1Suppose we examine the scores on the first test for Suppose we exam

9、ine the scores on the first test for students in MAT 205 from past semesters.students in MAT 205 from past semesters.Clearly this is quantitative data,and as such,a Clearly this is quantitative data,and as such,a histogram of the scores is appropriate.histogram of the scores is appropriate.Using Min

10、itab,the following histogram was Using Minitab,the following histogram was produced.Notice the bars are equal width,the produced.Notice the bars are equal width,the heights of the bars give the number of scores in heights of the bars give the number of scores in each interval,etc.each interval,etc.D

11、escribing Quantitative Data-HistogramsHistogram Example#1 QuestionsThere are many questions you should be able to There are many questions you should be able to answer from this type of graph.answer from this type of graph.What are the largest and smallest values possible in What are the largest and

12、 smallest values possible in the data set?the data set?Are there any unusual data points(called outliers)?Are there any unusual data points(called outliers)?Where do most values lie in the data set(if Where do most values lie in the data set(if appropriate)?appropriate)?What is the shape of the hist

13、ogram(if appropriate)?What is the shape of the histogram(if appropriate)?Histogram Example#1 QuestionsFrom the graph,the largest rectangle is centered at From the graph,the largest rectangle is centered at 100,and includes values from 95 to 105.Since I 100,and includes values from 95 to 105.Since I

14、know the exam scores had a maximum of 100 know the exam scores had a maximum of 100 points,I would conclude the largest values in the points,I would conclude the largest values in the data set were somewhere between 95 to 100 points.data set were somewhere between 95 to 100 points.Similarly,the smal

15、lest interval covers scores from 15 Similarly,the smallest interval covers scores from 15 to 25.Hence,the lowest score on the exam was to 25.Hence,the lowest score on the exam was between 15 and 25 points.between 15 and 25 points.There are no data points by themselves,so I would There are no data po

16、ints by themselves,so I would say there are no atypical values(outliers).say there are no atypical values(outliers).Histogram Example#1 QuestionsMost scores were between 75 and 95 as these were Most scores were between 75 and 95 as these were the tallest rectangles.The the tallest rectangles.The mos

17、t frequent categorymost frequent category has scores between 85 and 95.has scores between 85 and 95.Notice how there is only 1 rectangle to the right of Notice how there is only 1 rectangle to the right of the 75 to 95 range,but there are 6 rectangles to the the 75 to 95 range,but there are 6 rectan

18、gles to the left of the 75 to 95 range.This indicates the data left of the 75 to 95 range.This indicates the data stretches farther to the left than to the right.stretches farther to the left than to the right.We describe the shape as We describe the shape as skewed to the leftskewed to the left.Ske

19、wed to the leftSkewed to the leftSkewed to the rightSkewed to the rightSymmetricSymmetricSection 2.4-DefinitionsA A populationpopulation is the collection of is the collection of allall the data that the data that could be observed in a statistical study.could be observed in a statistical study.A A

20、samplesample is a collection of data chosen from the is a collection of data chosen from the population of interest.It is some smaller portion of population of interest.It is some smaller portion of the population.the population.An An inferenceinference is a decision,estimate,prediction,or is a deci

21、sion,estimate,prediction,or generalization about a population based on generalization about a population based on information contained in a sample from that information contained in a sample from that population.population.Section 2.4-ExamplesPopulationPopulationAll NKU students All NKU students Al

22、l votersAll votersenrolled during enrolled during in the 2004in the 2004summer 2004summer 2004electionelectionSampleSample500 NKU students 500 NKU students 2500 voters2500 votersenrolled duringenrolled duringin the 2004 in the 2004 summer 2004summer 2004electionelectionInferenceInferenceThe mean time toThe mean time toAbout 45%About 45%drive to NKU is drive to NKU is of voters of voters 24 minutes24 minutesfavor Kerry.favor Kerry.Press Esc to return