Stem and Leaf Plots
167640064770Stem and Leaf Plots4000020000Stem and Leaf PlotsAlgebra 2 CPName__________________Stats Notes 119050-3175Mean:Median:Mode:Range:00Mean:Median:Mode:Range:388429564770StemLeaf 00StemLeaf EXAMPLE 1Make a Stem and Leaf Plot for the following data set. 21, 18, 17, 18, 22, 46a. What are the highest and lowest numbers?b. What is the mean? c. What is the median? d. What is the mode? e. What is the range of numbers?4150995129540StemLeaf567893 6 85 80 3 7 7 91 4 8 8 99 8/4 represents 8400StemLeaf567893 6 85 80 3 7 7 91 4 8 8 99 8/4 represents 84EXAMPLE 2Answer the questions based on the given Stem and Leaf Plota. What are the highest and lowest numbers?b. What is the mean? c. What is the median? d. What is the mode? e. What is the range of numbers?EXAMPLE 3Answer the questions based on the given Stem and Leaf Plot434657570485StemLeaf192021223 5 52 2 5 85 8 8 9 9 90 1 7 8 9 19/5 represents 19.500StemLeaf192021223 5 52 2 5 85 8 8 9 9 90 1 7 8 9 19/5 represents 19.5a. What are the highest and lowest numbers?b. What is the mean? c. What is the median? d. What is the mode? e. What is the range of numbers?EXAMPLE 4The Stem and Leaf Plot below shows the height (in feet) of buildings in San Francisco.434657570485StemLeaf78910113 52 2 40 4 7 95 84 6 10/5 represents 105 ft.00StemLeaf78910113 52 2 40 4 7 95 84 6 10/5 represents 105 ft.a. What are the highest and lowest numbers?b. What is the mean? c. What is the median? d. What is the mode? e. What is the range of numbers?1676400647705 Number Summary40000200005 Number SummaryAlgebra 2 CPName__________________Stats Notes 219050-3175Range:Quartiles:Upper Quartile:Lower Quartile:Interquartile Range:00Range:Quartiles:Upper Quartile:Lower Quartile:Interquartile Range:19050158750Outlier:Outlier Number:Upper Fence:Lower Fence:00Outlier:Outlier Number:Upper Fence:Lower Fence:EXAMPLEFind the Five Number Summary, the Ranges, and the Outlier Fences for each of the following sets of data. If there are outliers, name them.a. 13, 15, 25, 22, 18, 19290512590805RANGESRangeIQR00RANGESRangeIQR454533090805OUTLIER FENCESOutlier NumberLower FenceUpper Fence00OUTLIER FENCESOutlier NumberLower FenceUpper Fence23050590805FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number00FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest NumberOutliers:______________________b. 107, 57, 47, 40, 34, 20, 25, 37, 46, 57, 69290512590805RANGESRangeIQR00RANGESRangeIQR454533090805OUTLIER FENCESOutlier NumberLower FenceUpper Fence00OUTLIER FENCESOutlier NumberLower FenceUpper Fence23050590805FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number00FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest NumberOutliers:______________________10541012065StemLeaf 81 9 92 3 6 101 9 112 4 8 9 123 700StemLeaf 81 9 92 3 6 101 9 112 4 8 9 123 7c. 4939665146685RANGESRangeIQR00RANGESRangeIQR2023110137160FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number00FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number454533022225OUTLIER FENCESOutlier NumberLower FenceUpper Fence00OUTLIER FENCESOutlier NumberLower FenceUpper Fence10 │ 1 represents 101Outliers:______________________106680144145StemLeaf 00 2 3 11 7 9 22 3 5 6 33 4 4 5 9 40 7 8 800StemLeaf 00 2 3 11 7 9 22 3 5 6 33 4 4 5 9 40 7 8 8d. 4939665146685RANGESRangeIQR00RANGESRangeIQR2023110137160FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number00FIVE NUMBER SUMMARYSmallest NumberLower QuartileMedianUpper QuartileLargest Number454533022225OUTLIER FENCESOutlier NumberLower FenceUpper Fence00OUTLIER FENCESOutlier NumberLower FenceUpper Fence4 │ 7 represents 47Outliers:______________________1695450-28575Box and Whisker Plots4000020000Box and Whisker PlotsAlgebra 2 CPName__________________Stats Notes 3190508890Box and Whisker Plot FormationDots are placed on the upper and lower _____________________ and ____________________ and the___________________________A ____________________________ box is made with the ends going through the ________________and ____________________ quartilesA vertical line is drawn _____________________ the box through the _____________________Two ___________________ lines are drawn to connect the quartile dots with the extreme dots00Box and Whisker Plot FormationDots are placed on the upper and lower _____________________ and ____________________ and the___________________________A ____________________________ box is made with the ends going through the ________________and ____________________ quartilesA vertical line is drawn _____________________ the box through the _____________________Two ___________________ lines are drawn to connect the quartile dots with the extreme dotsEXAMPLE 1 40767008636000Answer each question for the box and whisker plot to the righta. What are the upper and lower extremes?412432511112545 55 65 75 85 95 10502000045 55 65 75 85 95 105b. What is the median?c. What are the upper and lower quartiles?d. What is the interquartile range?EXAMPLE 2Speeds of the fastest train runs in the U.S. and Canada are given below in miles per hour. Make a box-and-whisker plot of this data.93.582.589.583.881.886.83581400850900090.884.995.083.183.288.2EXAMPLE 3Compare box and whisker plots A and Ba. What is the median of each data set?6848475123825AB020000AB35909258509000b. What is the least value in plot A?c. What is the greatest value in plot B?d. Which plot has the greater interquartile range?36957004889520 30 40 50 60 70 8002000020 30 40 50 60 70 80e. What is the lower quartile of each data set? f. What is the upper quartile of each data set?g. Which plot illustrates the larger range of data? h. What percent of the data in plot A is greater than 60?i. What percent of the data in plot B is less than 40?EXAMPLE 4Use the data to complete the following22 23 27 22 33 47 24 25 33 37 28 28 17a. Graph the data on a stem and leaf plot. b. Transfer the data to a vertical box and whisker plotStemLeaf335915013208000301561538735203040506070800020304050607080c. What are the extremes?d. What is the interquartile range?e. Why are the whiskers unequal?167640064770Normal Distribution4000020000Normal DistributionAlgebra 2 CPName__________________Stats Notes 419050-3175Normal Distribution:Standard Normal Distribution:Normal Curve:Standard Deviation:00Normal Distribution:Standard Normal Distribution:Normal Curve:Standard Deviation:115506513335First things first, if you have a Normal Distribution and know its mean and standard deviation, then you can calculate the probability of being anywhere within that distribution.? This is the same as answering the question:? "How likely is it to draw a value of X from this distribution?"00First things first, if you have a Normal Distribution and know its mean and standard deviation, then you can calculate the probability of being anywhere within that distribution.? This is the same as answering the question:? "How likely is it to draw a value of X from this distribution?"The normal curve is a graphical representation of probability – otherwise known as the “bell curve”. There are several things to remember: 15240019875568%95%99.7%z = -1z = 1z = 0z = -2z = -3z = 2z = 30068%95%99.7%z = -1z = 1z = 0z = -2z = -3z = 2z = 3 What does this all mean? Most outcomes will be within 3 standard deviations of the mean.243205-194310Z ScoreThe _________________ for an item indicates how far and in what _______________that item ____________________ from its distribution’s _________________The Z-Score is expressed in units of its distribution’s standard deviation and can be found by the formula:Z-Scores are sometimes called _______________________ ___________________The Z-Score Transformation is especially useful when seeking to compare the relative standings of times from distributions with different means and/or different standard deviations. 00Z ScoreThe _________________ for an item indicates how far and in what _______________that item ____________________ from its distribution’s _________________The Z-Score is expressed in units of its distribution’s standard deviation and can be found by the formula:Z-Scores are sometimes called _______________________ ___________________The Z-Score Transformation is especially useful when seeking to compare the relative standings of times from distributions with different means and/or different standard deviations. Standard Normal TableZ.0.1.2.3.4.5.6.7.8.9-3.0013.0010.0007.005.003.002.001.0001.0001.0000+-2.0228.0179.0139.0107.0082.0062.0047.0035.0026.0019-1.1587.1357.1151.0968.0808.0668.0548.0446.0359.0287-0.5000.4602.4207.3821.3446.3085.2743.2420.2119.18410.5000.5398.5793.6179.6554.6915.7257.7580.7881.81591.8413.8643.8849.9032.9192.9332.9452.9554.9641.97132.9772.9821.9861.9893.9918.9938.9953.9965.9974.99813.9987.9990.9993.9995.9997.9998.9998.9999.99991.0000-.0000+ means slightly more than 01.0000- means slightly less than 1EXAMPLE 1 – Using Normal Distribution CurvesUsing the normal distribution identify the mean and the standard deviation-517525292100037134808191500a.b.4592955151130130 144 158 172 186 200 21400130 144 158 172 186 200 214583565151130 156.85 166.2 175.55 184.9 194.25 203.6 212.9500 156.85 166.2 175.55 184.9 194.25 203.6 212.95-15240133985Using Your Calculator for Standard DeviationStep 1: Select STAT and 1:EDIT to enter the values into L1 individually hitting ENTER after each one Remember you can delete any entry with the DEL button Step 2: Find the MEAN by using 2nd STAT and moving to the MATH menu Then select option 3:MEAN and hit ENTER. Your screen should say “mean(” Hit 2nd 1 and hit enterStep 3: Find the STANDARD DEVIATION by using 2nd STAT and moving to the MATH menu Then select option 7:stdDev and hit ENTER. Your screen should say “stdDev(” Hit 2nd 1 and hit enter00Using Your Calculator for Standard DeviationStep 1: Select STAT and 1:EDIT to enter the values into L1 individually hitting ENTER after each one Remember you can delete any entry with the DEL button Step 2: Find the MEAN by using 2nd STAT and moving to the MATH menu Then select option 3:MEAN and hit ENTER. Your screen should say “mean(” Hit 2nd 1 and hit enterStep 3: Find the STANDARD DEVIATION by using 2nd STAT and moving to the MATH menu Then select option 7:stdDev and hit ENTER. Your screen should say “stdDev(” Hit 2nd 1 and hit enterEXAMPLE 2 – Using Your CalculatorUse the following information to calculate the mean and the standard deviationa. 14, 15, 17, 17, 19, 21, 23b. 178, 193, 204, 211, 211, 216, 177, 173, 168EXAMPLE 3 – Normal Distribution PercentagesWhat percentage is represented by the shaded region of the curve?384238510350500199390762000a.b.EXAMPLE 4 – Creating a Normal DistributionUse the following information to construct a normal distribution.a. The math scores for the 2004 SAT are b. A group of women were found to have normally distributed with a mean of 518 heights that are normally distributed and a standard deviation of 114. with a mean of 64.5 inches and a standard deviation of 2.5 inches.EXAMPLE 5 Use the normal distributions you created in example 4 to answer the following questions.a. What percentage of test takers have scoresb. What percentage of test takers have within 2 standard deviations above the scores that are more than 1 standard mean? below the mean?c. What percentage of women are mored. What percentage of women are 1 or than 3 standard deviations lower than more standard deviations above the the mean? mean?EXAMPLE 6 – Finding Z-ScoresCalculate the z –scores using the information from example 4 to answer the following questions.a. What is the probability of scoring at mostb. What is the probability of having a 653 on the SAT? woman at most 70 inches tall?1436370-95250Select and DrawConclusions from Samples020000Select and DrawConclusions from SamplesAlgebra 2 CPName________________________11.4 NotesDate_________________________-3810014605PopulationSamples00PopulationSamples514350080645001685925806450034099508064500-381008064500EXAMPLE 1 – Classify SamplesDetermine the sample style portrayed in the following examples.a. A manufacturer wants to sample the parts from a production line for defects. The manufacturer has every 5th item on the production line tested for defectsThe manufacturer has the first 50 items on the production line testedb. A computer science teacher wants to know if students would like the morning announcements posted on the school’s website.He surveys students in one of his computer science classes.He selects 50 names off of the master student list by closing his eyes and picking them from a hat-3810067945Bias in SamplingUnbiased SampleBiased Sample00Bias in SamplingUnbiased SampleBiased SampleEXAMPLE 2 – Identify a Biased SampleDetermine whether or not the following samples are biased or unbiased and briefly explain why.a. The manager of a concert hall wants to know how often people in the community attend concerts. The manager asks 50 people standing in line for a rock concert how many concerts per year they attend.b. A magazine asked its readers to send in their responses to several questions regarding healthy eating.-7620028575Margin of ErrorYou need to make sure that your sample size is large enough so that it accurately represents the population its being used to represent. As sample size ________________________, the margin of error ______________________The ______________________ of ______________________ gives a limit on how much the responses ofthe sample would differ from the responses of the ________________________00Margin of ErrorYou need to make sure that your sample size is large enough so that it accurately represents the population its being used to represent. As sample size ________________________, the margin of error ______________________The ______________________ of ______________________ gives a limit on how much the responses ofthe sample would differ from the responses of the ________________________2004695128905Margin of Error for Sample Size n:4000020000Margin of Error for Sample Size n:EXAMPLE 3 – Find a Margin of Errora. In a survey of 1011 people, 52 % said that television is their main source of news. A. What is the margin of error for the survey? B. Give an interval that is likely to contain the exact percent of all people who use their television as their main source of newsb. In a survey of 1535 people, 48 % preferred Brand A over Brand B and Brand C A. What is the margin of error for the survey? B. Give an interval that is likely to contain the exact percent of all people who prefer Brand Ac. In a survey of 1202 people, 11% said that they use the internet or e-mail more than 10 hours per week. A. What is the margin of error for the survey? B. How many people would need to be surveyed to reduce the margin of error to ±2%d. A polling company conducts a poll for a U.S. presidential election. How many people did the company survey if the margin of error is ±5% ................
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