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# Stat 200 - WEEK 2 SUMMARIZING AND GRAPHING

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Date Created: 11/05/15

WEEK 2 SUMMARIZING AND GRAPHING DATA Complete this guide on your computer as you read CHAPTER 21 and 22 In Chapter 2 we are going to look at sets of data and explore ways of analyzing that data so that conclusions can be made from that data Now it is possible to have a data set that has many as 100 data points or even 1000 s of data points We need to summarize this data in a way that makes the results more obvious and understandable One way to summarize the data is by using a frequency table If you look at Table 21 Academy Awards there is a lot of data Granted it is organized beginning with the first awards ceremony BUT the results are not obvious at a glance Now look at Table 22 Here the results are more direct We can immediately see that most of the award winners were between the ages of 31 and 40 This is a simple FREQUENCY table How many actresses were 4150 years old when they won 12 How many actresses were 5160 years old when they won 2 How many actresses were 4160 years old when they won 14 Now look at Table 23 This is the same information but now expressed as a percentage Relatively speaking this table gives us an even better idea of the data Now we know 39 of the actresses were between the ages of 31 and 40 when they received their awards This is a RELATIVE FREQUENCY table Magazine publishers love relative frequency tables because they can present information without having to list any confusing or maybe compromising data sets By the same token the reader has to trust that the publisher has data sets that are accurate and representative of their claims What of actresses were 4150 years old when they won 16 What of actresses were 5160 years old when they won 3 What of actresses were 4160 years old when they won 19 Now look at Table 28 COMPARATIVE RELATIVE FREQUENCY tables are even more fun to use We can fairly readily see that young actresses are more likely to win an award but actors can eXpect that they will have to prove themselves for a longer period of time before winning any award Assuming the data is correct then we might be able to conclude that males and females are not necessarily judged by the same sets of rules by the Oscar Awards Committees A comparative relative frequency table allows us to critically evaluate the data Any gap in the data larger than 5 is considered significant I What of actresses were 4150 years old when they won I 16 What ofaetors were 4150 years old when they won 39 What is the discrepancy between the two groups 15 Now you can go ahead and read pages 50 53 and then complete the matching question below with respect to Table 2 2 Lower class limit 213141516171 Upper class limit 30 40 50 60 70 80 Class boundaries 305 405 505 605 705 separates the classes Class midpoints 255 355 455 555 655 755 middle of each class Class width maximum minimum classes 80 21 6 10 If you were able to select the correct matches with no problem great if the concept is still a little confusing then try reading the definitions and examples below Class boundaries For some reason this concept usually takes a little longer to absorb Use the following information to complete the table below Take the lower class limit of one class let39s say 51 and take the upper class limit of the previous class 50 and subtract the smaller number from the larger So lower class limit previous upper class limit 51 50 1 Then take that difference between the classes 1 and divide by 2 So the mean difference is 12 05 Now go back to the first class 60 51 Subtract 05 from the lower class limit 51 05 505 and add 5 to the upper class limit 60 05 605 So we get 505 605 as the class boundaries around the actual class 51 60 Proceed in the same way to get the class boundaries for each class HINT The upper class limit of one class boundary is always the SAME as the lower class limit of the next class boundary To see this as a diagram see Figure 2 1 Lower boundary limit Class Upper boundary limit 305 31 40 405 405 41 50 505 5 05 51 60 605 605 61 70 705 Class Midpoint Add the lower class limit 51 and the upper class limit 60 and then divide the sum by 2 So 51602 1012 555 The class mark can also be interpreted as the midpoint mar or the Class Mark Class Width Besides using the formula provided maXimum minimum classes the class width can be described as the lower class limit of one class minus lower class limit of the previous class ie 51 41 10 This is usually easier to remember NOTE The class boundaries in conjunction with the class midpoints are used to make a histogram picture of frequency and relative frequency tables See Figures 2 2 and 2 3 for examples These histograms make the data even more obvious Our goal in this Chapter is to be able to create lovely histograms SAVE YOUR WORK PERIODICALLY AND TAKE A WELL EARNED BREAK NORMAL DISTRIBUTIONS In Science and in Math a NORMAL distribution is usually expected to be a fairly symmetrical BELL CURVE Read pages 54 56 A normal distribution implies a simple data set with no complicating factors An abnormal distribution implies something has skewed the expected data Our job is often to determine what that something is EXCEL Now follow the instructions on pages 56 58 to practice how to use EXCEL to construct a frequency distribution and a histogram Note the following changes to the instructions 1 The instructions assume that you will be using the data provided for Actress Ages in Table 2 1 You do not have to use these to test the system but if you do you should produce tables identical to the examples given on pages 57 and 58 5b If you want to create a Bin Range these values must appear on your worksheet prior to Data Analysis Note that you will be using the UPPER CLASS LIMITS only in EXCEL The instructions have you placing the Bin Range in column B but you could just as well place it in any column and just change the site accordingly For example if you placed the values in column C then you would enter the range ClC6 in stead of BlB6 as given in the example Practice using EXCEL to create a frequency table 22 Basic Skills and Concepts Before you proceed with the reading you might want to practice what you have learned You can place the answers to the following selected questions below The fill in tables have been constructed for you here and in TH to give you more time for practice work At the end of WEEK 2 the TAKE HOME assignment TH2 will be posted TH2 assignment will consist of a selected number of the practice problems assigned here Remember to save this CLASS NOTES file periodically as you are working into your STATS folder and once again before you close it You can HIGHLIGHT then COPY and PASTE the requested components of your completed work directly into the TAKE HOME assignments All future CLASS NOTES and TH assignments will be set up in this manner to save a little time and to have you practice the concepts you have just read about immediately Please ask questions as you work on the materials so that I can give you timely responses and information Remember that the odd numbered questions are answered in the back of your text and in your Student s Solution Manual as examples CHAPTER 22 222 223 225 Note Please use a calculator and refer to the formulas above p 2 if needed and show the formula you chose to use for class width below Some data has been PARTIALLY entered for you What is the class width formula Classes Daily Class Class Frequency EXCEL EXCEL Temperatures Boundaries Midpoint BIN Format Frequency in 9F 35 39 1 40 44 3 45 49 445 495 47 5 49 5 50 5 4 1 1 55 5 9 7 60 64 7 65 69 1 226 Note You will use the same formulas for decimals as whole numbers just be careful to enter each number accurately What is the class width formula Classes Daily Precipitation in inches Class Boundaries Class Midpoint Frequency EXCEL BIN Format EXCEL Frequency 000 049 050 099 100 149 150 199 1495 1995 1745 199 200 249 250 299 HONOH 227 Note You are now working backwards from the EXCEL FORMAT to create the frequency table Check the Student Solutions Manual for the example to start the chart and then complete it on your own Check the manual again to see if your calculations were correct Some sections are finished for you but others are only partially done so be sure to complete them What is the class width formula Classes Class Boundaries Class Frequency EXCEL EXCEL Height inches Midpoint BIN Format Frequency 600 649 5995 6495 6245 4 649 4 650 699 6495 6995 6745 25 699 25 749 7495 749 9 799 7995 799 1 849 8495 849 0 899 8995 899 0 949 9495 949 0 999 9995 999 0 1049 10495 1049 0 1099 10995 1099 1 228 Use what you have learned in the previous three examples to complete this chart What is the class width formula Classes Plastic Class Class Frequency EXCEL EXCEL Weigh in lbs Boundaries Midpoint BIN Format Frequency 099 8 1 99 12 299 6 399 0 499 0 599 0 699 0 799 5 899 15 900 999 8995 9995 9495 20 999 20 Whenever possible do not just answer a question with a YES NO or MAYBE also explain WHY Questions Answer Why 2 2 9 2 2 10 A B 2 2 11 A B C 2 2 12 A NOW IS A GOOD TIME FOR A COFFEE BREAK RELATIVE FREQUENCIES Relative frequency for each class can be found by dividing its frequency by the sum of the frequencies If you find the sum of all the relative frequencies it should be close to 1000 if you have used enough decimal points If you round the numbers up however occasionally the sum of the relative frequencies will be a tiny bit less than or more than 1000 ie 9997 or 10001 2 2 13 Temp C F Frequency Relative Frequency 35 39 1 40 44 3 45 49 5 50 54 1 1 55 59 7 60 64 7 65 69 1 Sum Sum 2 2 14 Rain Frequency Relative Frequency 000 049 31 050 099 1 100 149 0 150 199 2 200 249 0 250 299 1 Sum Sum Now let us put what you have learned to practical use We will look at a very popular chemical used in today s society Nicotine You will use your EXCEL program to manipulate the data and then transfer the results to the tables below For question 2 2 20 the Data set on STATDISK is called CIGARET Select only the Nicotine data for this exercise and copy and paste it into your new EXCEL file You will next create your 8 classes and enter the upper limit of each class into column B of your EXCEL worksheet before you can used the DATA ANALYSIS function under TOOLS To create the classes requested you must 1 Determine how many classes you want to have 8 Usually you want to keep this number below 10 so the data is easy to work but you can have more 2 Find the lowest value in the data set 3 If the lowest value is close to zero assume it to be zero 0 or select a lower value that is convenient to use based upon the number of classes you wish to have 4 Find the highest value in the set 5 If the highest value is not convenient to use you can choose a slightly higher number based upon how many classes you want to have and their width 6 Determine the class width Given in the question The 02 width must be in useable logical even increments In this case we know the class width must increase by increments of 02 since the directions are explicit If our first lowest class limit is zero then our next lowest class limit must be 02 and the third lowest class limit must be 04 These values have been entered for you in the table below Finish the lower class limits until all 8 are present Next you must determine the upper class limit for each of the 8 classes remember that the classes cannot overlap So you cannot for example have 00 02 for the first class since 02 is already used in Class Two The upper limit of Class One must be greater than 00 and less than 02 plus it must have the same number of decimal places as the lower class limit You could use 00 01 or you could also use 000 099 or 0000 0999 depending upon the data Which do you think would be the most logical simplest to use in this case Place all your selected upper class limits into the table below Review your classes to see if they are logical and then copy the only UPPER CLASS LIMITS UCLs into your EXCEL file in column B Question 2 2 20 Nicotine Classes Relative uenc 00 02 04 After transferring the UCLs use your EXCEL program and the TOOLS DATA ANALYSIS HISTOGRAM functions to determine frequency Once you have the frequencies just copy and paste them into the table above Find the sum of the frequencies and then calculate the relative frequencies for each class using your calculator Describe the nature of the distribution of nicotine classes Is the frequency distribution a NORMAL distribution Yes or No and WHY If nicotine concentrations of 14 mg or higher can cause lung cancer what of the selected population is at risk For further practice try using your EXCEL program and do the odd numbered questions using your Student s Solutions Manual as a guide 23 HISTOGRAMS A histogram is a picture of a frequency or relative frequency table where the X aXis usually has the class boundaries or class midpoints and the y aXis uses the frequencies The histograms for the Ages of the Best Actresses are present in Figures 2 2 and 2 3 on page 62 Note how the class boundaries make the range distribution continuous One can determine the distribution of the data by looking at the histogram For example complete the following frequency table by calculating the Relative Frequency Grade of Students Number of Students A 4 B 9 C 10 D 3 F l To fill a cell with color select the cells and then select the paint bucket on your tool bar to fill the cells with any color you choose The first one is done for you If you do not see a paint bucket select VIEW TOOLBARS and then check TABLES AND BORDERS 10 C Grades Note that the shape of the histogram resembles a bell shape so it is a normal distribution If a frequency table of grades has a skewed shape See Figure 2 2 then the entire class may be very smart or the instructor is just being too nice A relative frequency histogram will appear to have the same distribution as a frequency histogram The only difference is that the y aXis scale will be marked with a distribution instead of actual frequencies Read pages 63 66 and follow the directions to create histograms using EXCEL Instead of using the Actresses ages you can copy and paste the nicotine data from the EXCEL worksheet that you used for question 2 2 20 You can copy and paste your completed Histogram below Be sure to adjust the size of the histogram to fit the page comfortably NOTE THE FOLLOWING CHANGES TO INSTRUCTION 8 1 Some programs do NOT have the TEXT BOX icon In this case you can right click on the graph and select CHART OPTIONS to modify your chart titles aXis legend and grid lines 2 Use the Class midpoints see the sample histogram below for the midpoints instead of the Class boundary values You can enter these into the frequency table you generated when creating the Histogram The BIN and FREQUENCY table should magically appear to the left of your Histogram When you change the table the Histogram also changes Your histogram should be similar to the one shown below except the background will be white instead of gray 3 When you have completed your sample histogram copy and paste it below Sample Histogram Histogram FHUUI IV 1 1 05 025 045 065 085 105 125 145 More Nicotine in mg PASTE YOUR NICOTINE HISTOGRAM BELOW NOTE You can eliminate lines below your pasted graphs by clicking below the graphs and BACKSPACING You can also change the size of your graphs by clicking on the graph and on the comer boxes and dragging the graph handles to the size you want 23 Basic Skills and Concepts Hints Answer 2 3 5 Add the column frequency values 2 3 6 Find class width Determine the Min range for each class for the midpoints MaX given 2 3 7 A coxswain directs the rowers only The rowers do the actual work 2 3 8 Subtract two consecutive midpoints Create a Histogram for Question 2 3 15 Weights of Pennies using Data set 14 in Appendix B EXCEL Data set COINS Paste your Histogram below this line HINT Choose 5 classes for your frequency with the Upper Class Limits and midpoints provided below when creating your graph Weights of Pre1 983 Pennies UCL Midpoints 300 2975 3 305 3025 310 3075 298 303 208 313 318 Weight gran1s 10 315 3125 320 3175 PLACE YOUR HISTOGRAM FOR 2315 HERE You have created the histograms for Question 2 3 12 Nicotine and Question 2 3 15 Weights of Pennies immediately above Now answer the questions pertaining to them below Answer Yes or No and explain Why 2 3 12 2 3 15 TIME FOR A REALLY NICE PIECE OF CHOCOLATE CAKE AND TEA OR PERHAPS CHIPS AND PEPSI g4 STATISICAL GRAPHICS This section introduces various types of graphing techniques including Frequency Polygons Ogives Dotplots Stemplots Pareto Charts Pie Charts Scatter diagrams and Timeseries graphs As you read through this section follow the EXCEL practices You will not remember all the instructions the first time around but remember that if you are in asked in the future to create a certain type of graph all you have to do is go to the INDEX of this text and find the page number that provides the detailed instructions OR you can use the HELP guides which are included in the EXCEL program The goal of this exercise is to become familiar with the various graph types and to be able to not just create graphs but be able to critically interpret them as well FREQUENCY POLYGON Follow the directions on page 70 and create a Frequency Polygon After step 7 you will want to create Titles for your graph Rather than using EXCEL steps 8 and 9 on page 65 you can follow the instructions to the right of the sample polygon Save your work Sample Frequency Polygon 11 Frequency Polygon 255 355 455 555 655 755 Ages of Best Actresses Right click on the graph and choose CHART OPTIONS Select TITLES Type in the titles for the Chart X and Y aXis and then select OK Click the white background of the chart COPY and PASTE your frequency polygon below The sample provided has a blue gradient background Your chart will have a plain gray background but if you wish you can change the color to any color texture background you wish other than the sample To do this click on the chart and select FORMAT PLOT AREA and then select your desired colors PASTE YOUR FREQUENCY POLYGON HERE RELATIVE FREQUENCY POLYGON Now you can create a relative frequency polygon with the Actress and Actors data sets You will be doing this slightly differently Transfer the relative frequency data in the table below to your EXCEL file Actresses Actors 0 O 37 4 39 33 16 39 3 18 3 4 3 1 O O Relative Frequency Polygon Actresses Actors 255 355 455 555 655 755 Agesin years 12 Once the data is in EXCEL then HIGHLIGHT the entire set Select INSERT CHART LINE to make the graph appear Select SERIES and adjust the X aXis labels to read space255 355455555655755space and then click NEXT Give your graph appropriate TITLES Relative Frequency Polygon for Chart Title for the Value Y aXis and Age in years for the Category X aXis Select GRID and remove the gridlines but leave the Legend Click FINISH Once the graph appears in EXCEL you can modify it 9 Click on the Legend ActressesActors and drag it up 10 Click on the side of the gray graph and stretch the graph to the right 11 Click on the Legend again to position it in the top right comer of the graph 12 Click on the white area of the graph and COPY and then PASTE it below U PPJNE 90gt PASTE YOUR RELATIVE FREQUENCY POLYGON HERE OGIVE OHJ IVE Look at Figure 2 6 for now Instructions for creating this graph come later in the course Estimate how many of the Actresses were younger than 305 years of age DOTPLOTS Look at the dotplot at the top of page 72 How many of the Actresses were older than 72 years of age STEMPLOTS Read about Stemplots This is a different way of looking at data It is like a vertical histogram only the bar now actually consists of the single digit numbers leaves on the stem class Look at the stemplot at the bottom of page 72 13 I How many of the Actresses were 60 years of age or older All three charts use the same data but present it in different formats I Which plot type did you like the best STEMPLOTS To better understand a stemplot you will now create your own You will use heights of the eruption of Old Faithful geyser listed in Data Set 11 of Appendix B EXCEL FILE OLDFAITHXLS to construct a stemplot using the table below When you are done you can check the answer to 2 4 9 in your Student s Solution Manual or Appendix F of your text to see if you were correct Remember that the STEM may consist of several digits but the LEAVES are the last digit only of each number and must appear in chronological order For example if a number is 45 then the Stem is 40 and the leaf is 5 If you have the numbers 41 44 44 45 then the Stem is 40 and the leaves are l445 NOTE If a number is 45089 then the stem is 45080 and the leaf is 9 2 4 9 Now enter the heights of Old Faithful Stem Leaves 2 4 6 Let us repeat the exercise using Data Set 8 Actual High Temperatures in Appendix B Create your Stem Leaf chart using the table below Stem Leaves l4 If you rotate the computer screen counterclockwise 90 degrees then you will have your histogram Isn39t that cool The main advantage of a stem and leaf plot over a histogram is that the data can be recreated from the stem and leaf plot From the histogram the data cannot be recreated PARETO CHARTS Flowers inaPark These charts are nice to use for 39 qualitative data where the one aXis represents frequency or relative frequency and the other ads uses words instead of numbers Follow the f directions on page 74 to create your own 0 1000 2000 3000 4000 5000 6000 chart and then paste it below You can Numbers quot959 be inventive with the data PASTE YOUR PARETO CHART HERE PIE CHARTS Flowersinapark These charts are also fun to do You can use the same data that you used for your Pareto Chart or Daisy Aster 15 Petunia Orchids Ra esia you can use any other data that appeals to you Follow the directions on page 75 to create your chart NOTE Add the following steps to the instructions 25 Highlight the data set 85 Under Data Labels select Category name PASTE YOUR PIE CHART HERE SCATTERPLOTS Scatterplots are often used to determine if there is a relationship between two variables Usually a relationship eXists between two sets of values if a curved or straight line can be drawn among the points The straighter the line the better the relationship In the scatterplot on Page 76 there is definitely a relationship between temperature and chirps per minute since one could draw a diagonal line from the bottom left corner of the graph to the top right corner and see that most of the points fall on either side of the line If you draw the same line on the graph on page 77 you will see that most of the points fall at one end of the line or the other so in effect there are no points in the middle region In this case there is some other factor involved than just weight I What do you think the other factor is l6 Now you will create your own Scatterplots following the direction on page 75 Use the data sets in questions 2 4 17 and 2 4 18 to create your scatterplots NOTES FOR SCATTERPLOTS 1 If you highlight the two columns of data before you click INSERT the program will automatically enter the data into the graph so you will not have to manually insert your columns A22A3O or B22B30 2 If you select CHART OPTIONS you can enter the titles and other features 3 If you click on the graph you can also select FORMAT CHART AREA to alter Tar and CO content of cigarettes color and style PASTE YOUR SCATTERPLOT FOR QUESTION 2417 HERE 2417 Is there a relationship between TAR and CO Give a reason QUESTION 2418 In EXCEL you can cut and paste the data columns where you wish For a scattergram the X aXis horizontal aXis is always the left column and the y aXis vertical aXis is always the right column Copy data set 9 into your new EXCEL file and rearrange the data columns so that the temperature column is to the left of the kWh column The simplest way to do this is to copy and paste the information from the original data set to a new location in your file 17 Once this is done if you highlight both columns and then go to INSERT CHART then the program will automatically incorporate the data selected Then all you have to do is modify your chart using CHART OPTIONS Electric Usage and Daily Temperature 3500 3 o 3 3000 5 A D g 6 3 5 2500 o h O n O D 2000 25 35 45 55 65 Average daily temperatures F 75 NICE TOUCHS YOU CAN ADD You can modify the SCALE of your graph to better fit the data by 0 RIGHT clicking on the X aXis and then selecting FORMAT AXIS and SCALE and then setting the MINIMUM value for the X aXis to 25 0 Repeating the process you can select the minimum value for the y aXis as 2000 PASTE YOUR SCATTERPLOT FOR QUESTION 2418 HERE 2418 Is there a relationship between kWh and daily temperature Give a reason TIMESERIES GRAPHS Time series graphs are extremely popular with companies which monitor sales over several years If you look at the graph on page 78 you can see that the popularity of drive in movies has declined abruptly and then stabilized l8 What year was data first collected How many driveins were present in 1968 How many driveins were present in 1997 Use the directions on page 78 to create your own time series graphs 500 400 300 200 100 IIIIIJGI 40000 35000 30000 25000 20000 15000 10000 5000 IIVUIIVU IIIIUVI VI I Runwav near hits C T 01 co d U D 0 0 0 0 0 0 0 0 0 0 0 0 O 0 391 1 1 391 1 391 1 Year W 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Year 1997 Use the data sets provided in questions 2 4 19 and 2 4 20 for your graphs Your results should look somewhat like the sample graphs shown Note that I have left the graph lines in both graphs Your instructions however ask you to remove the graph lines Please do so 1998 1999 Remember to save your work Indoor Movie Theatres PASTE YOUR TIMESERIES GRAPH FOR QUESTION 2419 HERE l9 Graph 2 4 19 Runway Near Hits Is there a trend If so what is it PASTE YOUR TIMESERIES GRAPH FOR QUESTION 2420 HERE Graph 2 4 20 Indoor Movie Theatres Is there a trend If so what is it How does this trend compare to the Drivein movie theatres p 78 Read pages 79 82 If you are interested in purchasing vehicles stereos or any other expensive consumer goods then you probably have seen charts similar to Figure 2 9 p 79 There is a lot of data contained in it but it is very easy to use 20 If you like medicine then look carefully at Florence Nightingale s chart in Figure 2 10 and if you like history then look at the chart on page 81 Before you Close this file and your book save all the work you have done in your STATS file on your computer 21

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