Descriptive_Statistics

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George Washington University *

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Statistics

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Apr 3, 2024

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xlsx

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Part1-chickwts_dataset Part1- Types of Data in Excel - Text, Numbers, Date/Time, Logical Descriptive Statistics Part2- Installing Data Analysis Pack and Calculating Descriptive Statistics Part3- measure of central tendency/ variation Part4- visualization Probability Distribution
Description Usage mtcars Format [, 1] mpg Miles/(US) gallon [, 2] cyl Number of cylinders [, 3] disp Displacement (cu.in.) [, 4] hp Gross horsepower [, 5] drat Rear axle ratio [, 6] wt Weight (1000 lbs) [, 7] qsec 1/4 mile time [, 8] vs V/S [, 9] am Transmission (0 = automatic, 1 = manual) [,10] gear Number of forward gears [,11] carb Number of carburetors Source Motor Trend Car Road Tests The data was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). A data frame with 32 observations on 11 variables. Henderson and Velleman (1981), Building multiple regression models interactively. Biometrics , 37 , 391–411.
mpg cyl disp hp drat Mazda RX4 21 6 160 110 3.9 Mazda RX4 Wag 21 6 160 110 3.9 Datsun 710 22.8 4 108 93 3.85 Hornet 4 Drive 21.4 6 258 110 3.08 Hornet Sportabout 18.7 8 360 175 3.15 Valiant 18.1 6 225 105 2.76 Duster 360 14.3 8 360 245 3.21 Merc 240D 24.4 4 146.7 62 3.69 Merc 230 22.8 4 140.8 95 3.92 Merc 280 19.2 6 167.6 123 3.92 Merc 280C 17.8 6 167.6 123 3.92 Merc 450SE 16.4 8 275.8 180 3.07 Merc 450SL 17.3 8 275.8 180 3.07 Merc 450SLC 15.2 8 275.8 180 3.07 Cadillac Fleetwood 10.4 8 472 205 2.93 Lincoln Continental 10.4 8 460 215 3 Chrysler Imperial 14.7 8 440 230 3.23 Fiat 128 32.4 4 78.7 66 4.08 Honda Civic 30.4 4 75.7 52 4.93 Toyota Corolla 33.9 4 71.1 65 4.22 Toyota Corona 21.5 4 120.1 97 3.7 Dodge Challenger 15.5 8 318 150 2.76 AMC Javelin 15.2 8 304 150 3.15 Camaro Z28 13.3 8 350 245 3.73 Pontiac Firebird 19.2 8 400 175 3.08 Fiat X1-9 27.3 4 79 66 4.08 Porsche 914-2 26 4 120.3 91 4.43 Lotus Europa 30.4 4 95.1 113 3.77 Ford Pantera L 15.8 8 351 264 4.22 Ferrari Dino 19.7 6 145 175 3.62 Maserati Bora 15 8 301 335 3.54 Volvo 142E 21.4 4 121 109 4.11 Mean 20.090625 *Slides class 1 Standard Dev for Population 5.93202955230123 denominator = n Standard Dev for Sample 6.02694805208912 denominator = n-1 mpg 20.090625 20.090625 wt
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Mean 3.21725 Standard Error 0.17296847326012 Median 3.325 Mode 3.44 Standard Deviation 0.9784574429897 Sample Variance 0.95737896774194 Kurtosis 0.41659466963493 Skewness 0.46591610679299 Range 3.911 Minimum 1.513 Maximum 5.424 Sum 102.952 Count 32 -7.335574904E-133
wt qsec vs am gear carb 2.62 16.46 0 1 4 4 2.875 17.02 0 1 4 4 2.32 18.61 1 1 4 1 3.215 19.44 1 0 3 1 3.44 17.02 0 0 3 2 3.46 20.22 1 0 3 1 3.57 15.84 0 0 3 4 3.19 20 1 0 4 2 3.15 22.9 1 0 4 2 3.44 18.3 1 0 4 4 3.44 18.9 1 0 4 4 4.07 17.4 0 0 3 3 3.73 17.6 0 0 3 3 3.78 18 0 0 3 3 5.25 17.98 0 0 3 4 5.424 17.82 0 0 3 4 5.345 17.42 0 0 3 4 2.2 19.47 1 1 4 1 1.615 18.52 1 1 4 2 1.835 19.9 1 1 4 1 2.465 20.01 1 0 3 1 3.52 16.87 0 0 3 2 3.435 17.3 0 0 3 2 3.84 15.41 0 0 3 4 3.845 17.05 0 0 3 2 1.935 18.9 1 1 4 1 2.14 16.7 0 1 5 2 1.513 16.9 1 1 5 2 3.17 14.5 0 1 5 4 2.77 15.5 0 1 5 6 3.57 14.6 0 1 5 8 2.78 18.6 1 1 4 2 There is a shorter version for descriptive analysis Data Analysis Pack Need to install it once PC. File>Option>add-ins>Data tab> Mac. Tools>Excel add-ins>Data tab> hp Mean 146.6875
Standard Error 12.1203173116 Median 123 Mode 110 Standard Deviation 68.5628684893206 Sample Variance 4700.86693548387 Kurtosis 0.2752115875371 Skewness 0.7994066925956 Range 283 Minimum 52 Maximum 335 Sum 4694 Count 32
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mpg Miles/(US) gallon cyl Number of cylinders disp Displacement (cu.in.) hp Gross horsepower drat Rear axle ratio wt Weight (1000 lbs) qsec 1/4 mile time vs V/S am Transmission (0 = automatic, 1 = manual) gear Number of forward gears carb Number of carburetors
mpg cyl disp hp drat wt Mazda RX4 21 6 160 110 3.9 2.62 Mazda RX4 Wag 21 6 160 110 3.9 2.875 Datsun 710 22.8 4 108 93 3.85 2.32 Hornet 4 Drive 21.4 6 258 110 3.08 3.215 Hornet Sportabout 18.7 8 360 175 3.15 3.44 Valiant 18.1 6 225 105 2.76 3.46 Duster 360 14.3 8 360 245 3.21 3.57 Merc 240D 24.4 4 146.7 62 3.69 3.19 Merc 230 22.8 4 140.8 95 3.92 3.15 Merc 280 19.2 6 167.6 123 3.92 3.44 Merc 280C 17.8 6 167.6 123 3.92 3.44 Merc 450SE 16.4 8 275.8 180 3.07 4.07 Merc 450SL 17.3 8 275.8 180 3.07 3.73 Merc 450SLC 15.2 8 275.8 180 3.07 3.78 Cadillac Fleetwood 10.4 8 472 205 2.93 5.25 Lincoln Continental 10.4 8 460 215 3 5.424 Chrysler Imperial 14.7 8 440 230 3.23 5.345 Fiat 128 32.4 4 78.7 66 4.08 2.2 Honda Civic 30.4 4 75.7 52 4.93 1.615 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 Toyota Corona 21.5 4 120.1 97 3.7 2.465 Dodge Challenger 15.5 8 318 150 2.76 3.52 AMC Javelin 15.2 8 304 150 3.15 3.435 Camaro Z28 13.3 8 350 245 3.73 3.84 Pontiac Firebird 19.2 8 400 175 3.08 3.845 Fiat X1-9 27.3 4 79 66 4.08 1.935 Porsche 914-2 26 4 120.3 91 4.43 2.14 Lotus Europa 30.4 4 95.1 113 3.77 1.513 Ford Pantera L 15.8 8 351 264 4.22 3.17 Ferrari Dino 19.7 6 145 175 3.62 2.77 Maserati Bora 15 8 301 335 3.54 3.57 Volvo 142E 21.4 4 121 109 4.11 2.78 mpg Formula you can use to calculate the summary statistics on Mean 20.090625 AVERAGE AVERAGEA AVERAGEIF AVERAGEIFS Standard Error 1.06542396 STDEV.S/SQRT(n) Median 19.2 MEDIAN Mode 21 MODE.SNGL MODE.MULT Standard Deviation 6.02694805 STDEV.P STDEV.S VAR.P VAR.S
Sample Variance 36.3241028 STDEVPA STDEVA VARPA VARA Kurtosis -0.02200629 KURT Skewness 0.67237714 SKEWP SKEW Range 23.5 MAX-MIN 23.5 Minimum 10.4 MAX 33.9 Maximum 33.9 MIN 10.4 Sum 642.9 SUM Count 32 COUNT *slides class 1 Measure of Central Tendency Measure of Dispersion/spread The concept of Standard Error will come once we rea to Inferential Statistics. Standard Error is the Standard Deviation divided by the square root of a total number of items here. So if this was a sample of 32 and you wanted to calculate what's the Standard Error. STDEV.S(mpg)/ SQRT(32) Skewness and Kurtosis are related to the Shape in reference to normal distribution. Always remember: Skew is related to the long tail. v Skew = 0 means perfect symmetric v Skew between 0 and +/- 0.5 means approximately symmetric v Skew between +/- 0.5 and 1.0 means moderately skewed v Skew more than +1 or less than -1 means highly skewed v Normal distribution has Kurtosis = 0 v Kurtosis < 0 means peak is short and broad, tails are shorter v Kurtosis > 0 means peak is higher and thinner, tails are longer 3 2
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qsec vs am gear carb 16.46 0 1 4 4 17.02 0 1 4 4 18.61 1 1 4 1 19.44 1 0 3 1 17.02 0 0 3 2 20.22 1 0 3 1 15.84 0 0 3 4 20 1 0 4 2 22.9 1 0 4 2 mpg 18.3 1 0 4 4 cyl 18.9 1 0 4 4 disp 17.4 0 0 3 3 hp 17.6 0 0 3 3 drat 18 0 0 3 3 wt 17.98 0 0 3 4 qsec 17.82 0 0 3 4 vs 17.42 0 0 3 4 am 19.47 1 1 4 1 gear 18.52 1 1 4 2 carb 19.9 1 1 4 1 20.01 1 0 3 1 16.87 0 0 3 2 17.3 0 0 3 2 15.41 0 0 3 4 17.05 0 0 3 2 18.9 1 1 4 1 16.7 0 1 5 2 16.9 1 1 5 2 14.5 0 1 5 4 15.5 0 1 5 6 14.6 0 1 5 8 18.6 1 1 4 2 ne by one ctrl-shift-enter array AverageA, AverageIf, and Averageifs. -Average: will give me the Average of all these values in B2 to B33. -Average A: takes care of the text such as True or False and gives the value of 1 to the True and the value of 0 to the False which. just in case you come across the situation where you want to keep the value of True as one and the value of False as zero, this will be Averaging that. -AverageIf: averageif is when we want to put a condition. 1
like averagea when you have text in data -0.022006291 0.6723771376 in excel you can give name to the cell or a range. select the range > right click> define name> exp:cyl exp Functions (formulas): SUM 642.9 Add all the numbers in the range SUMIF 293.3 Adds the cells specified by a given condi SUMIFS 0 Adds the cells specified by a given sets o AVERAGE 20.090625 4 cyl AVERAGEIF 26.6636364 AVERAGEA 4 cyl / auto AVERAGEIFS #DIV/0! condition. exp, we can find the value of the average mpg for four cylinder engine, six cylinder engine and eight cylinder engine, so you can add one condition that the number of cylinders is equal to four, six or eight which are in column number C. a -Averageifs: where you can have a multiple ifs there we put this value of cylinder as four and then we look at that automatic and manual version of that what is the difference in mpg. ach mmetric wed d orter onger
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Miles/(US) gallon Number of cylinders Displacement (cu.in.) Gross horsepower Rear axle ratio Weight (1000 lbs) 1/4 mile time V/S Number of forward gears Number of carburetors Transmission (0 = automatic, 1 = manual)
ition or criteria - exp: sumif mpg if cyl=4 of conditions
Student Number Height 1 162 2 160 100 students 3 158 lets first find the highest and lowest value 4 162 doing descriptive statistics 5 159 6 164 * tip: to select the complete column takr ctrl+shift+down arrow 7 160 8 158 Column1 9 163 10 161 Mean 159.73 11 166 Standard Error 0.28279092466115 12 161 Median 160 13 170 Mode 159 14 161 Standard Deviation 2.82790924661148 15 163 Sample Variance 7.99707070707072 16 161 Kurtosis 2.05641592388702 17 160 Skewness 0.04295753487117 18 159 Range 20 19 160 Minimum 150 20 159 Maximum 170 21 156 Sum 15973 22 160 Count 100 23 159 24 160 25 161 26 161 27 154 28 163 29 158 30 160 31 159 32 159 33 150 34 165 35 161 36 154 37 159 38 161 39 159 40 161 41 158 42 159 43 159 44 161
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45 162 46 160 47 162 48 161 49 158 50 159 51 157 52 156 53 159 54 165 55 156 56 162 57 158 58 159 59 160 60 155 61 163 62 157 63 161 64 163 65 161 66 158 67 158 68 162 69 163 70 159 71 157 72 159 73 158 74 154 75 160 76 161 77 157 78 159 79 161 80 160 81 156 82 161 83 156 84 161 85 158 86 160 87 159 88 160 89 160
90 159 91 157 92 158 93 156 94 156 95 158 96 164 97 162 98 163 99 161 100 164
creating bins in order to create histogram we can say this is a normal distribution then go to Data Analysis pack, select histogram and the height of students are normally dist looking at descriptive statistics and compare Bin Bin Frequency 150 150 1 152 152 0 154 154 3 156 156 8 158 158 17 160 160 32 162 162 25 164 164 10 166 166 3 168 168 0 170 170 1 More 0 second way of creating histogram in MS>201 Insert>histogram>select data Series1 0 5 10 15 20 25 30 35 Histogra Bin Frequency This chart isn't available in your version of E Editing this shape or saving this workbook i break the chart.
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Wisker Plot example tributed e 16 Insert>wisker plot>select data am Frequency Excel. into a different file format will permanently This chart isn't available in your version of Excel. Editing this shape or saving this workbook into a diffe format will permanently break the chart.
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erent file
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temp sales 24 201 Scatter Plot to show relationship between 2 diagrams 30 400 outside temperature and Icecream sales 16 185 as heats goes up, we sell more icecream. Is there a re 26 332 15 155 28 522 select the whole data with columns 25 412 insert > charts > Scatter 21 422 29 544 22 421 17 301 24 408 21 345 32 473 21 385 34 532 19 295 31 603 26 528 independent variable is on X axis = temp dependant variable is on y axis = sales double Click on chart> select Chart Elements > and se Now we can talk about the correlation double Click on chart> Chart Elements > trend line > *slide11 class2 10 15 20 25 30 0 100 200 300 400 500 600 700 R² = 0.621352917756286 f(x) = 18.1597155487219 x − 47.7699 sales sales of icecreams
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here means that temprature explain 62% variation of there are other factors that have effect on sales that
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s elationship? elect trend lin win + more option > R2 35 40 9404189889 10 15 20 25 30 35 0 100 200 300 400 500 600 700 f(x) = 18.1597155487219 x − 47.7699404189889 R² = 0.621352917756286 sales
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f the sale we don't know or cant get from this data
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40
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Which height range has the most number of students? How many students have height less than 152 cm?
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In the below Box-and-Whisker Plot there are three points indicated by th What is the condition for a point to be shown as outlier in Box and Whis there are other factors that have effect on sales that we don't know or cant get from this data A number which is less than Q1 or greater than Q3 by more than A number which is more than 1.5 times the median A number which is more than 1.5 times the Q2 How many ice creams are expected to be sold, when the maximum temp
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he red arrow. What are these points called? sker Plot? 1.5 times the IQR range perature is 30 C?
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