Community Colleges in Houston | San Jacinto College



Statistics Boot Camp: Student PacketStatistics BasicsThe data represents the cost of gas in 2005 for a sample of 20 vehicles:13 15 15 8 16 20 28 19 18 1521 23 30 17 10 16 15 16 20 15Construct a frequency distribution for the data set using five classes:ClassFrequencyMidpointRelative FrequencyBoundariesCumulative FrequencyRemember: Class Width = Range# of classes = Max-Min# of classesClass Boundaries = Upper limit of the 1st class-(lower limit of the 2nd class)2Frequency: Is how often a number occurs within a class.Midpoint = Upper limit of the 1st class+(Lower limit of the 2nd class)2Relative Frequency = Frequency Total FrequencyCumulative Frequency: You add each frequency by the sum of the frequency of the preceding class.The data represents the hourly earnings (in dollars) of sample of 15 medical professionals.39 36 30 27 26 24 28 35 39 60 50 41 35 32 51Find the following:Five-number summaryIQROutliersBox-and-whisker plotRemember:a)Min “Minimum” = lowest numbered sample in the setMax “Maximum” = highest numbered sample in the setQ1 “Quartile 1” = Is the middle value in the first half of the data set.Q2 “Quartile 2” = medianQ3 “Quartile 3” = Is the middle value in the second half of the data set.b)IQR “Interquartile Range” = Q3 - Q1c)Outliers: Must be calculated for “Outliers less than” and “Outliers more than.”“Outliers less than” = Q1 – (1.5 * IQR)“Outliers more than” = Q3 + (1.5 * IQR)d)Box-and-Whisker plot:Plot all calculated data on a Box-and-Whisker plot11. The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.2 10 15 4 15 8 15 9 4 7 The range is: _______The population mean is: __________ (Round to the nearest tenth as needed.)The population variance is: ________ (Round to the nearest hundredth as needed.)The population standard deviation is: ___________ (Round to the nearest tenth as needed.)Remember:Range = Max – Min? “Population mean” = Sum of all numbers in data settotal numbers in data setσ2 “Population Variance” = Take the square of the standard deviation.σ “Population Standard Deviation” = The square root of the variance.The ages (in years) of a random sample of shoppers at a gaming store are shown. Determine the range, mean, variance, and standard deviation of the sample data set.12 19 23 15 18 18 21 18 14 16The range is: _______The population mean is: __________ (Round to the nearest tenth as needed.)The variance is: ________ (Round to the nearest hundredth as needed.)The standard deviation is: ___________ (Round to the nearest tenth as needed.)Range = Max – Min? “Population mean” = Sum of all numbers in data settotal numbers in data setσ2 “Sample Variance” = Take the square of the sample standard deviation.σ “Sample Standard Deviation” = The square root of the sample variance.The 7 Graphs commonly used in Statistics:Qualitative Data Charts:Are the Pie Chart and the Pareto Diagram.Construct a Pie Chart from the data:Type of degree in 2020Number “in 1000’s”Relative FrequencyRelative Frequency %Angle in degreesAssociates942Bachelors1716Masters731Doctoral164Remember:Relative Frequency = Frequency Total FrequencyRelative Frequency % = Frequency Total Frequency * 100%Angle in degrees = (Relative Frequency %) * 360°Construct a Pareto Diagram from the data:A company lost a total 34.4 billion.Employee theft 15.1Shoplifting 12.3Vendor fraud 1.7Administrative error 4.2Unknown 1.1Must remember: Qualitative data only applies to pie charts and Pareto diagramQuantitative charts:Are the Stem and Leaf Plot, Dot Plot, and Histogram:Construct a Stem and Leaf Plot from the data:23 55 23 54 24 52 26 33 31 32Construct a Dot Plot from the data:23 55 23 54 24 52 26 33 31 32Construct a Histogram from the data:13 15 15 8 16 20 28 19 18 1521 23 30 17 10 16 15 16 20 15ClassFrequencyBoundariesRemember: To mention skewness.Paired Data Charts:Are the Time Series Graph and the Scatter plot:Construct a Time Series Graph from the data:YearCrime “murders”196039196552197879198375199085Construct a Scatter Plot from the data:Temperature in °FSale of Ice Cream322254325053275723408051095730 Empirical Rule:For the data sets with distribution approximately symmetric and bell shaped, the standard deviation has these characteristics:So, in other words, this is that about 68 percent of the values lie between?z-scores of –1 and 1, about 95% of the values lie between?z-scores of –2 and 2, and about 99.7 percent of the values lie between?z-scores of -3 and 3. These facts can be checked, by looking up the mean to?z?area in a?z-table for each positive?z-score and multiplying by 2.Find the indicated area under the curve. Round to four decimal places.To the left of z = .08To the right of z = -.65Between z = 0 and z = 2.86Find the indicated probabilities using the standard normal curve. Round to four decimal places.P(z < 1.45)P(z > -.18)P( -1.65 < z < 1.65 )Tips and Tricks – Do’s and Don’ts of Calculator:The Do’s:Texas Instruments TI - 84 Plus CE: Casio FX-115 ES Plus: Best Software Calculator!!!TI SmartView CE for the TI – 84 Plus Family:The Don’ts:Texas Instruments TI-83 series calculatorsTexas Instruments TI-30 series calculatorsTexas Instruments TI-nSpire calculatorsCasio FX-9750 GII calculatorCasio G series calculators ................
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