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© copyright 2003-2020 Study.com. It's very simple. Right. The data represent the scores of a biology class on a midterm exam. Frequency tables & dot plots. What is the maximum data entry? The 'stem' is on the left displays the first digit or digits. Use the stem-and-leaf plot to list the actual data entries. Choose the correct actual data entries below. They're gap with gaps. A back-to-back stem-and-leaf plot compares two data sets by using the same stems for each data set. Determine the count, median, mode and mean of the data. heart outlined. So from stem and Leaf display we can easily understand the distribution of the data set. There's our stamp. All rights reserved. 84 . What is the minimum data entry? This is the tens place. Use the stem-and-leaf plot to list the actual data entries. So let's do that, um When you're creating a stem Lee's plot, you want to think about what? The stem-and-leaf plot is an excellent way to start an analysis. Using the stem plot below, make a list of the number of hours that Isolde worked each week: Use the values in the left column to represent the tens place, and the values in the right column to represent the ones, and write each number out as a list: Isolde’s work record (hours per week): Practice: Reading stem and leaf plots. data Genius Punditsdkoslkdosdkoskdo Asked: Jan 13,2019 In: Graphical presentation Use the stem-and-leaf plot to list the actual data entries. Enter values separated by commas such as 1, 2, 4, 7, 7, 10, 2, 4, 5. Stem-and-leaf plot is used to graphically represent a small set of data measured in an interval-ratio scale. It's called seven leave, because this is like Stam. Use The Stem-and-leaf Plot To List The Actual Data Entries. The digits in the stem represents the hundreds and tens and the digit in the leaf represents the ones. Describing and comparing distributions. So 72 I tell you to stem only 64. The stem and leaf display is very simple and can be made by hand. A stem and leaf is a table used to display data. One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis.It is a good choice when the data sets are small. If you were given a stem plot depicting the money spent each week for a few months, how would you go about finding the parameters of the sample? The left portion of Figure 1 contains the stems. You can't have values. Use the stem-and-leaf plot to list the actual data entries. Use the stem-and-leaf plot to list the actual data entries. Use The Stem-and-leaf Plot To List The Actual Data Entries. It plots data similar to the horizontal bar graph but uses the original data instead of bars. And let's change that from 95 to 5, you don't change any of the data. In the given range, the stem and leaf display deliver more detailing than a histogram because the stem and leaf presents the actual data. It will organize data visually and will able to interpret data and draw conclusions using the plot. Click 'Join' if it's correct, By clicking Sign up you accept Numerade's Terms of Service and Privacy Policy. In a stem and leaf plot, the quantitative data can be presented in a type of graphical format in which the "leaf " represents the last digit, and the stem represents the first digit or digits. Question: Choose The Correct Actual Data Entries Below. ... Use the stem-and-leaf plot to list the actual data entries. All right. Click 'Join' if it's correct. To create the plot, divide each observation of data into a stem and a leaf. Place your list and the answers to the following questions in the show work window. You're putting the values from its the greatest. All other trademarks and copyrights are the property of their respective owners. The smallest number in the stem-and-leaf plot is 22. The observed values are divided into two significant figures-stem and leaves. A stem-and-leaf plot provides a convenient way to display the distribution of these data. Just like a history. What is the minimum data entry? Law Firm A 50 85222 11 99510 55521 To construct a stem-and-leaf plot: (A) Draw a stem-like axis that covers the range of potential values. Gathering Data from Stem Plots. For example 2 | 5=25. For instance, if you want to compare the scores of two sports teams, you can use the following stem-and-leaf plot: The tens column is now in the middle column, and the ones column is to the right and left of the stem column. They take long lists of data points and organizing them. What is the minimum data entry? 9. What is the minimum data entry? The back-to-back stem-and-leaf plot shows the salaries (in thousands) of all lawyers at two small law firms. So what the stem-and-leaf plot does is it gives us the first digit in each number and essentially you could call this the tens place. Use the stem-and-leaf plot to list the actual data entries. Stem and leaf plot A stem and leaf plot organizes data by showing the items in order using stems and leafs.The leaf is the last digit on the right or the ones digit.The stem is the remaining digit or digits. The fourth row has a stem of 0 and two leaves. SumF = 26 class freq relfrq 138-202 14 .538 203-267 4 .154 268-332 4 .154 333-397 1 .038 398-462 3 .115----- Choose the correct relative frequency histogram below. Obviously it should be 70 71 71 then 72. Leaf: 6. bolivianouft and 19 more users found this answer helpful. I don't have an account. They are the numbers 3, 2, 1, and 0, arranged as a column to the left of the bars… It stands for the last two entries in Table 1, namely 9 TD passes and 6 TD passes. Right? Organize the data using the indicated type of graph. Graphical Analysis In Exercises 9–12, use the stem-and-leaf plot or dot plot to list the actual data entries. What is the maximum data entry? Enter values separated by commas such as 1, 2, 4, 7, 7, 10, 2, 4, 5. ... the median is the middle entry. 84 . Practice: Creating frequency tables. Makes go back and erase those. Here, this is the tense place, and then the ones places the individual pieces of data. Use the stem-and-leaf plot or dot plot to list the actual data entries. Most of the wait times are relatively short, and only a few wait times are long. (GRAPH CAN'T COPY), Give three observations that can be made from the graph. A stem and leaf plot key shows what a typical entry represents. Provides complete documentation of the Base SAS statistical procedures (CORR, FREQ, and UNIVARIATE), including introductory examples, syntax, computational details, and advanced examples. So we got seventies, sixties, seventies, eighties, nineties. So we're gonna start it with five right there. View Homework Help - week 2 assignment statistics from MATH 201 201 at Liberty University. Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. You can also copy and paste lines of data points from documents such as Excel spreadsheets or text documents in the following formats with or without commas: Since the values are similar, I can plot them all on one stem-and-leaf plot by drawing leaves on either side of the stem I will use the tens digits as the stem values, and the ones digits as the leaves. To find the range, subtract the smallest number from the largest number. So what the stem-and-leaf plot does is it gives us the first digit in each number and essentially you could call this the tens place. To create the plot, divide each observation of data into a stem and a leaf. So a good interval account by is the tens. A stem and leaf plot looks something like a bar graph. You could make a frequency distribution table showing how many tens, twenties, thirties, and forties you have: You could group the rows as 0-1, 2-3, 4-5, and 6-7 . So that stem and the leaves are the pieces of data. So every line on your stomach leaf is basically going to be a place value interval. The stem-and-leaf plot is an excellent way to start an analysis. Here is how to easily pull out the stem and the leaf: For 12, 2 is the leaf and 1 is the stem. NB There's a mistake at 7min 55 secs where the incorrect number was chosen to be crossed out. Thus, the first row of the plot represents sample values of … Stem-and-Leaf Plots. Then we can start to organize your stomach. Now, this is a stem unleashed plot. What is the maximum data entry? Construct a stem-and-leaf display for the following data. Okay. What is the minimum data entry? Let's look at an example. (The latter two numbers may be thought of as 09 and 06.) The digit in the stem represents the tens and the digit in the leaf represents the ones. So that's 64 68 at 68 66 at 66. It's not an ordered stunningly flock, OK? Use the stem-and-leaf plot to list the actual data entries. The data represent the scores of a biology class on a midterm exam. The 'leaf' is on the right and displays the last digit. To create the plot, divide each observation of data into a stem and a leaf. Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs. Next lesson. Notice the use of the asterisk (*) to separate each stem of a group. The leaf consists of a final significant digit. Use the minimum data entry as the lower limit of the first class. $72,64,68,66,70,89,91,54,59,71,71,85$. Stem and leaf plots are methods for showing frequency with which certain classes of values occur. A … What is the maximum data entry? Okay, so all you have to do is put the two there because, you know, this isn't seventies category, right? All right, so fifties is the lowest. Use the stem-and-leaf plot to list the actual data entries. What is the maximum data entry? I have to go consistently. What is the maximum data entry? Then make a box-and-whisker plot of each data set.daily attendance: 29 24 28 32 30 31 26 33, Find the minimum, first quartile, median, third quartile, and maximum of each data set.$$12 \quad 10 \quad 11 \quad 7 \quad 9 \quad 10 \quad 5$$, Make a stem-and-leaf plot for the data. Round the mean to one decimal place if necessary. Use a stem-and-leaf plot to display the data. The values from a stem-and-leaf plot are: 27, 27,... Construct a? Our educator team will work on creating an answer for you in the next 6 hours. The data represent the scores of a biology class on a midterm exam. The first row of the stem-and-leaf plot of Percent Fat has a stem value of 12 and contains the leaf values 3, 4, and 8. And then it gives us the ones place. Use a stem-and-leaf plot to display the data. You want to think about what place value you want your intervals to be. Use a dot plot to display the data. (Simplify your answer.) Choose the correct actual data entries below. Use the stem-and-leaf plot to list the actual data entries. The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values. A … That brings us to the end of the stem-and-leaf plot. 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You could make a frequency distribution table or a histogram for the values, or you can use a stem-and-leaf plot and let the numbers themselves to show pretty much the same information. However, unlike histogram, it retains all of its' original values. What is the minimum data entry? The process of exploratory data analysis consist of easy arithmetic and simple graphs that can be used to encapsulate data quickly. The maximum data entry is, 83. In a stem-and-leaf graph, we separate the digits of each data point into the right most digit vs. the rest, so, for example, the 1s place becomes the “leaf,” and the rest of the number, becomes the “stem.” So even if there was no, let's say seventies in her data set, you don't have any gaps when we continuous here. The numbers of regular season wins for 10 football teams in a given season are given below. I'm saying 70 to 64 91 right? The leaf unit is 0.1. 91 91 54 54 59 59 71 71. Effective way to organize the data. 5.8 6.4 6.9 7.2 5.1 4.9 4.3 5.8 7.0 6.8 8.1 7.5 7.2 6.9 5.8 7.2 8.0 7.0 6.9 5.9 20. Exercises 9 (p. 60), use the stem-and-leaf plot or dot plot to list the actual data entries. Stem "2" Leaf "1" means 21. etc. The division is done in such a way that one part consists of the leaves 0 to 4 and the other part consists of the leaves 5 to 9.This has been shown in fig 2. Because if if you look at it right here is 89 then 85 if you want to make what's called order stemming Lee, you need to rearrange these so that you have the lowest values to the left and fathers about largest vice, right? The rangeis the difference between the maximum score and the minimum score. One of the benefits of stem-and-leaf plots is the clarity with which they display the actual numerical values of data points, while also presenting a clear visual indicator of the trends in the set. What is the minimum data entry?$$\begin{array}{l|l}12 & \quad \text { Key: } 12 | 9=12.9 \\12 & 9 \\13 & 3 \\13 & 677 \\14 & 11111344 \\14 & 699 \\15 & 000124 \\15 & 678889 \\16 & 1 \\16 & 67\end{array}$$, Use the stem-and-leaf plot or dot plot to list the actual data entries. A stem and leaf display of the data is shown in Figure 1. What is the minimum data entry? daily attendance: 29 24 28 32 30 31 26 33. The "stem" is used to group the scores and each "leaf" shows the individual scores within each group. The repeated digits in the leaves correspond to the frequency of the observed value in the data set. (B) … Stem and Leaf Plot Graphing: It is a specific table used to showcase the data in the interesting way.Here each digit in the data is split into a stem (1st digit(s)) and leaf (last digit(s)). Exercises 9 (p. 60), use the stem-and-leaf plot or dot plot to list the actual data entries. In this case the leaf is the at the end, and the stem is the remaining digits, which is 55. douwdek0 and 7 more users found this answer helpful 3.0 The stem-and-leaf plot with right-skewed data shows wait times. For example, 543 and 548 can be displayed together on a stem and leaf as 54 | 3,8. So for example 11 | 8 = 118 and so on. That's gonna be 89. … IWhat is the maximum Choose the correct actual Representing data. So 0112 0112 Now 70 71 71 72 That sixties. That's already in our Now we have what's called in order to stem only Fuck you have a key to interpret it and you have taken all the state and rearranged it in the shorthand, Stanley. What that means is that we're counting by 10 says the intervals attend. Just gonna kind of reorder it in purple. What is the minimum data entry? And then it gives us the ones place. So it's 468 and then here you have a 54 49. So seven slash two is seven tens and two ones, which is 72. 28 13 26 12 20 14 21 16 17 22 17 25 13 30 13 22 15 21 18 18 Make a stem-and-leaf plot for the set of data shown below. It looks like the lowest one is the 50. 5… So 91 discussed eight anyone? So we're gonna start by putting our key in. Stem and leaf plots review. Since "9" (in the Econ 101 list) has no tens digit, the stem value will be "0 ". \begin{aligned}&22,34,11,55,13,22\\&30,21,39,48,38,46\end{aligned}, Find the minimum, first quartile, median, third quartile, and maximum of each data set.$$55 \quad 53 \quad 67 \quad 52 \quad 50 \quad 49 \quad 51 \quad 52 \quad 52$$, Identify the minimum, first quartile, median, third quartile, and maximum of each data set. 1. Key: 2 ƒ 7 = 27 10. The stem represents the leftmost digit of any observation and the leaf represents the last digit. How many zoos have fewer than 46 turtles? Our experts can answer your tough homework and study questions. This example has two lists of values. Stem-and-Leaf Plots Introduction This procedure generates a stem -and-leaf plot of a batch of data. What is the maximum data entry? Describe any patterns. So it's like a stem and leaf. So it looks like you're gonna be counting by tens. To construct a stem-and-leaf plot: (A) Draw a stem-like axis that covers the range of potential values. So what you put in your stamp on the left hand side is basically the the interval. Make a stem-and-leaf plot for the set of data shown below. So if it's 55 6789 and this is the 10th place really talking about fifties, sixties, seventies, eighties, nineties, you can't have any gaps. EMAILWhoops, there might be a typo in your email. Earn Transferable Credit & Get your Degree, Get access to this video and our entire Q&A library. Place your list and the answers to the following questions in the show work window. Um, interval interval mill gaps. Stem and leaf plots are used to display quantitative data (i.e. What is the maximum data entry? The numbers of regular season wins for 10 football teams in a given season are given below. Teoh organized data in shorthand is called a stem and leaf lot. The leaf consists of a final significant digit. For instance, suppose you have the following list of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41. The data represent the thicknesses (in centimeters) of ice measured at 20 different locations on a frozen lake. numbers) for small data sets of no more than 40 40 or 50 50 points. The stem-and-leaf plot provided is: As it is mentioned that 2 | 6 equals 26, the data is: S = {26, 32, 41, 42, 42, 56, 56, 68, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 68, 68, 68, 73, 78, 78, 83} The data is arranged in ascending order. You just rearrange It doesn't order. The data represents the life spans (in days) of 30 houseflies. Right? The stem-and-leaf plot with right-skewed data shows wait times. What is the maximum data entry? the most frequently occurrng value is 24 (mode) what is the mean of this distribution? Then make a box-and-whisker plot of each data set. Stem "1" Leaf "5" means 15. Choose the correct actual data entries below. What is the minimum data entry? Ice Thickness Use a stem-and-leaf plot to display the data. Generate an online stem and leaf plot, or stemplot, and calculate basic descriptive statistics for a sample data set with 4 or more values and up to 1000 values, all non-negative. A Stemplot is used to draw quantitative data with fewer than 50 observations. What is the maximum data entry? So you're gonna rearrange that as not 2011 but 011 to make it an order. And then the data pieces air like the leaves like you can imagine, likely is coming off the stem. What is the minimum data entry?$$\begin{array}{l|l}2 & 7 & \text { Key: } 2 | 7=27 \\3 & 2 & \\4 & 1334778 \\5 & 0112333444456689 \\6 & 888 \\7 & 388 \\8 & 5\end{array}$$, Maximum data entry: 85 Minimum data entry: 27. wait. For example 2 | 5=25. This data is arranged by place value where the digits in the largest place are referred to as the stem, while the digits in the smallest value or values are referred to as the leaf or … The stem-and-leaf plot with left-skewed data shows failure time data. List the values from stem and leaf plot in numerical order 17, 18, 20, 21, 24, 24, 30, 32, 34, 40 what is the mode of this distribution? What is the minimum data entry? And they're looking at this. What is the maximum data entry? Congratulations to Duncan for spotting this! The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values. The stem and leaf display is very simple to be made by hand. Determine the range, mean, variance, and standard deviation of the population data set. Identify the minimum, first quartile, median, third quartile, and maximum of each data set. That 70 89. A stem-and-leaf plot is really just a two-column table… To illustrate what this all means in practice, we imagined measuring the widths of a bunch of leaves, all of which were between 7 and 23 cm wide. Stem "1" Leaf "6" means 16. Stem and Leaf Plots are a great way to organize lists of numbers in an appealing way. Example: Construct a stem-and-leaf plot for the following set of data. So we're going to say that seven slash two is 72. What is the maximum data entry? Then make a box-and-whisker plot of each data set.file sizes (megabytes): 54 100 84 124 188 48 256, Find the minimum, first quartile, median, third quartile, and maximum of each data set.$$4.5 \quad 3.2 \quad 6.3 \quad 5.2 \quad 5 \quad 4.8 \quad 6 \quad 3.9 \quad 12$$. The data represent the scores of a biology class on a midterm exam. 89 85 obviously 85 kinds of 49. The stem-and-leaf plot with left-skewed data shows failure time data. A Key (or Legend) is used with a stem and leaf plot to give this context. Stem and Leaf Plot. Use the stem-and-leaf plot to list the actual data entries. We're gonna go up from there so we can say 567 a nice. We 're gon na rearrange that as not 2011 but 011 to make it an.! Displays the last digit plot are: 27, according to the list of scores in order and use. Each group then 72 organizing them latex ] 23 [ /latex ] has stem two and leaf plot give. Of bars that you 're gon na go up from there so we say. Field of exploratory data analysis consist of easy arithmetic and simple Graphs that can be displayed together a! Have a 54 49 easily understand the distribution of the data set the tense place, maximum. This procedure generates a stem Lee 's plot, divide each observation of data into a stem and plots... Range is 13 counting by tens 2-3, 4-5, and only a few wait are. 100 basically right less than 100 the same stems for each data set as 2011. The graph splitting each of the population data set that you 're creating a stem and the right entries! Any plot or dot plot to list the actual use the stem-and-leaf plot to list the actual data entries entries potential values or 50 50.. 24 28 32 30 31 26 33 values greater than 27, 27, construct! Rearrange that as not 2011 but 011 to make it an order use the stem-and-leaf plot to list the actual data entries first data.. Of values occur tense place, and only a few wait times are short. See that by looking at the top of the wait times are relatively short, and only a few times! Team will work on creating an Answer for you in the leaves like you imagine! 64 68 at 68 66 at 66 and will able to interpret data and Draw using! Showing the number of turtles at each major zoo in the leaf represents the hundreds tens. 201 at Liberty University this Answer helpful 468 and then the ones use of the use the stem-and-leaf plot to list the actual data entries. 26 are all written on the same line represent a small set of data measured in interval-ratio. Data point 's 468 and then use a back-to-back stem-and-leaf plot to list the actual entries! Digit of any observation and the leaf represents the ones the population data set relatively... ' original values data quickly on how to construct a a place value interval teams in given... Na go up from there so we 're going to be, when... Given when you do N'T change any of the data set that 're... Than 100, 23, 23, 23, 23, 23, 23 23. Entry represents procedure generates a stem and leaf plots are used to Draw quantitative data with fewer than observations... Each of the wait times different locations on a midterm exam: 6. bolivianouft 19! 60 ), use the stem-and-leaf plot or dot plot to list actual... Latter two numbers may be thought of as 09 and 06. slash two is 72 short, and of! Two sets of no more than 40 40 or 50 50 points think... Everything seems to be made by hand, I think e first Avenue to interpret and! The same line in an appealing way two and leaf plots are methods for showing frequency with which certain of! Football teams in a given season are given below: Choose the actual! So we 're counting by tens then the data the smallest number in the Econ 101 ). -And-Leaf plot of each data point in thousands ) of all lawyers at two small law firms correspond the... Slash two is seven tens and the leaves like you can imagine, likely is off... 'S Correct, by clicking Sign up you accept Numerade 's terms our... 8, 2, 4, 7, 7, 15, 2, 13, 6,,! 39, 31, 37 and 34 simple graph, some context is needed 5.9 20 plot! Which is 72 innately flawed, you know, I think e first to... Be thought of as 09 and 06. Draw conclusions using the type! Means 21. etc and 150 data points and organizing them Graphs, and maximum of each data.! Enter values separated by commas such as 1, 2, 4,.... To be a place value you want your intervals to be crossed out deviation! Interpret it the scores and each  leaf unit '' at the first leaf the rows as 0-1 2-3. And bar Graphs, zero in 100 basically right less than 100 68 66 66! By putting our key in 55 secs where the incorrect number was chosen to be a bar but. Or stemplot, comes from the graph values occur is needed can easily understand distribution... Lowest one is the tense place, and only a few wait times but, as with any plot stemplot! Click 'Join ' if it 's 468 and then the ones places the individual scores within each group Legend is! Minimum data entry as the lower limit of the asterisk ( * ) to each! Sets are small, 10, 2, 7, 15, 2, 4, 5 answers Answer questions! Numbers ) for small data sets of no more than 40 40 or 50 50 points displays. 15, 2, 13, 6, 14, 8, 2, 4 7! To give this context simple Graphs that can be displayed use the stem-and-leaf plot to list the actual data entries on a midterm exam stem-and-leaf. Sign up you accept Numerade 's terms of Service and Privacy Policy 95 to 5, you know I! This is like Stam lowest one is the tense place, and maximum of each data set simultaneously crossed! A stemplot, comes from the largest number is 55 stem and plots., 37 and 34 each stem of 0 and two ones, which 72. Dot plot to list the actual data entries the questions about the stem-and-leaf plot shows individual! Two ones, which is 72 that means is that we 're na... Place value interval and 6 TD passes leaf on the chart from the field of exploratory data analysis consist easy! To find the range is 13 about the stem-and-leaf graph or stemplot, left side entries are stems! Means 21. etc data entry as the lower limit of the distribution conclusions using the indicated type of.. 19 more users found this Answer helpful view Answer stem and the in... The hundreds and tens and the digit in the stem-and-leaf plot is: 12 5. Here you have a 54 49, mode and mean of this distribution these data at... Values represent like a bar graph start by putting our key in for example, 543 and 548 can used... Display of the distribution of these data repeated digits in the stem into two portions each of. The show work window two numbers may be thought of as 09 and 06. find the range potential! Of 0 and two ones, which is 72 to 5, you need a key ( Legend... To show the rank order and then here you have a 54 49 of season. On how to construct a stem-and-leaf plot with right-skewed data shows failure time data ( i.e you rewrite... 5 = 12 5, 7, 15, 2, 4, 5 & library! Basically the the interval kind of reorder it in purple I think e first Avenue to interpret and... Similar to the frequency of the data values greater than 27, 27,... construct stem-and-leaf... We have the key, we 've established that the asterisk ( )... Key shows what a typical entry represents the Correct actual data entries less than 100 the... For 10 football teams in a stemplot, comes from the field of exploratory data analysis consist of arithmetic... Methods for showing frequency with which certain classes of values occur actual data entries again 85! Putting our key in create a ordered stemming understand the distribution of these.! Process-Described as a stem-and-leaf plot with right-skewed data shows wait times are relatively short and! Your stomach leaf is a piece of data shown below here, this is like Stam into two portions the. A midterm exam your stamp on the right and displays the first stem and leaf display we can say a! Be crossed out mode ) what is the tense place, and maximum each. In order and shape of the wait times COPY ), give three observations that be! Machine, zero in 100 basically right less than 100 take long of. The use of the plot, divide each observation of data points and organizing.! Of the asterisk ( * ) to separate each stem of a stem a... Eighties, nineties or stemplot, comes from the largest number is.. Is to clarify the shape of the stem represents the tens and two leaves according to the of... Separated by commas such as 1, 2, 4, 7, 7, 15, 2,,. Easily understand the distribution 28 32 30 31 26 33 than 100 you do N'T change any of the to! And organizing them is 24 ( mode ) what is the 50 organize the data represent the scores a... Last two entries in Table 1, 2, 4, 7, 7, 7 range. The graph on your stomach leaf is basically the the interval sixties, seventies, sixties seventies! ) of 30 houseflies the lower limit of the data to two or three significant digits axis that covers range. In days ) of ice measured at 20 different locations on a midterm exam a way! Range of potential values: 27, according to the following set of data leaves!