box plot questions worksheet

Primary Study Cards. This is the page for free maths worksheets and resources about box plots, reading them and plotting them. Box and Whisker Plots Statistics Day 2. The range is the smallest value subtracted from the largest value, so if we subtract the range from the largest value we will be able to work out the smallest value: The interquartile range is the lower quartile subtracted from the upper quartile, so if we add the interquartile range to the lower quartile, we will be able to work out the upper quartile: We now have all the information we need to plot the box plot. Box Plots. Browse our pre-made printable worksheets library with a variety of activities and quizzes for all K-12 levels. We are going to use the data sets we collected in class to create box and whisker plots. For questions 1 â 6, refer to the box & whisker graph below which shows the test results of a math class. Box and Whisker Plots with Student Worksheet is an introductory PowerPoint presentation teaching students what a Box and Whisker Plot is and how it can be used with data. The 25th value has a weight of 84 kilograms. Questions : 1. The reaction times for the 20-year-olds has been plotted below: The reaction times for the 30-year-olds are as follows: Construct a box plot for this set of the data and note two differences between the two groups. 1. The Corbettmaths Textbook Exercise on Box Plots. On the cumulative frequency graph, we need to locate 25 on the cumulative frequency axis and find the corresponding salary. 2. Open in new tab 4. The 50th value for Welsh Bank corresponds to a salary of £52,000, and the 50th value for the Bank of Finland corresponds to a salary of £62,000. 4. Since there are 100 values in total, the upper quartile is the 75th value (since 75 is \frac{3}{4} of 100. _____ 2. Which group has the greater variability in the bottom 50% of shopping times ? Also a couple of worksheets to allow students to get some independant practice, plus the data I collected from my year 9s that I got them to draw box plots from to compare my two year 9 classes. Use this information and the cumulative frequency to draw a box plot on the grid below. (2 Marks) The box plot below shows the amount spent by people over the Christmas period in 2015. b. Cumulative Frequency and Box Plot Practice Questions Click here for Questions . Question 2: A class of students sat an exam. Word problems are also included. Use this information to construct a complete box plot. A box plot (sometimes also called a âbox and whisker plotâ) is one of the many ways we can display a set of data that has been collected. Stem-and-Leaf /Box-and-Whisker Plots : Select the correct answer from the given alternatives, …, Box and Whisker Plot Worksheets with Answers : Learn how to calculate box and whisker plots, extreme values, fences, exercises, …. Make sure you are happy with the following topics before continuing. Find the minimum and maximum scores. Their total marks, out of a possible 100, were recorded. Test Scores (as %) for 9th Period 38 72 88 96 102 _____ 1. the salaries at Welsh Bank and Bank of Finland are equally consistent (since the interquartile range. First, we will go through what all the bits mean. The year 9 class also have a larger interquartile range. The weight of the lightest member was 61 kilograms and the weight of the heaviest member was 135. The median time is greater for the year 9 class. The Medians, Quartiles & Boxplots worksheet, along with actual SQA Exam Questions, are highly recommended. Find the median and describe what it means for the data. Browse our pre-made printable worksheets library with a variety of activities and quizzes for all K-12 levels. Box and whisker plot worksheet pdf with answers. Box plots worksheet A worksheet consisting of two GCSE past paper questions on interpreting box â¦ Question 4: The below cumulative frequency graph shows the weight of 100 people who attend Weight Watchers. Determine whether the following statements are TRUE or FALSE regarding this box plot. Quiz & Worksheet Goals. They will read and interpret box and whisker plots. Box-and-whisker plot worksheets have skills to find the five-number summary, to make plots, to read and interpret the box-and-whisker plots, to find the quartiles, range, inter-quartile range and outliers. Box and Whisker Plot Worksheets with Answers admin October 11, 2019 Some of the worksheets below are Box and Whisker Plot Worksheets with Answers, making and understanding box and whisker plots, fun problems that give you the chance to draw a box plot and compare sets of data, several fun exercises with solutions. Practice Questions; Post navigation. Box Plots questions for your custom printable tests and worksheets. Review Packet Answer Key Statistics and the Number System : Several Practice exercises. Keep the interest of learners alive with this pdf worksheet on outliers. Donât panic, these numbers are easy to understand. 11,12,12,13,14,14,14,16,18 Compare the box plots. Compare the shapes of the box plots. Find the interquartile range. On the graph, we need to locate 75 on the cumulative frequency axis and find the corresponding weight in kilograms. Directions: These questions deal with box and whisker plots. The first page gets students to work out the median and quartiles of a given (discrete) data set. Box Plots Quiz - Displaying top 8 worksheets found for this concept.. Draw a box plot for this information. Thank You, © 2021 DSoftschools.com. Interpreting a Box & Whisker Plot For questions 1 â 5, refer to the box & whisker graph below which shows the test results of a math class. Specifically, we are missing the upper quartile and the lowest value. The interquartile range is a good measure of spread because it is unaffected by any outliers – data points which sit far away from all the other. For Welsh Bank and for the Bank of Finland, it is £80,000. These printable exercises cater to the learning requirements of students of grade 6 through high school. Find and describe the lower and upper quartiles. Questions : 1. a) Draw two separate box plots to represent the spread of salaries at each bank. In a hurry? Search for: Contact us. To find the interquartile range we subtract the lower quartile (Q_1) from the upper quartile (Q_3). The 75th value has a weight of 101 kilograms. Previous Inequalities Practice Questions. Taking too long? Taking too long? These printable exercises cater to the learning requirements of students of grade 6 through high school. Since there are 100 values in total, the lower quartile is the 25th value (since 25 is \frac{1}{4} of 100. In this data interpretation worksheet, 6th graders make a box and whisper plot to represent a data set and complete 4 questions. To do this, we need the quartiles. The following are facts about the data recorded on the students’ scores. 2. You should be able to interpret box plots as well as construct them from given data. Mathematics Test : Several tests on Statistics and Probability, Geometry, Functions, …. Some of the worksheets below are Box and Whisker Plot Worksheets with Answers, making and understanding box and whisker plots, fun problems that give you the chance to draw a box plot and compare sets of data, several fun exercises with solutions. GCSE Higher: The box plot shows information about the distribution of the times (in minutes) groups of customers spend in a open-air restaurant. Range – The smallest shoe size was 1.5 and the largest was 13, from this we can calculate the range. As a result, the completed box plots should be similar to the two below: b) By comparing the two box plots, we can see that: We have a range of learning resources to compliment our website content perfectly. One advantage is that worksheets are very â¦ To find the highest salaries, we need to find what 100 on the cumulative frequency axis corresponds to. Box Plot Questions Worksheet Worksheets fun reading comprehension worksheets high school wh questions worksheets pdf 7th grade math problems and answers pdf present simple questions exercises pdf past simple questions exercises pdf Homeschool worksheets have pros and cons that depend on the type of material the worksheet deals with. TRUE. Videos, worksheets, 5-a-day and much more What was the high score on the test? Compare the centers of the box plots. Now we have all the necessary details to draw the box plot, which should be similar to this: Comparing the two box plots, we can see that the second one has a higher median, meaning that the 30-year-olds were on average slower at reacting than the 20-year-olds. Look at the following example of box and whisker plot: To construct a box plot, we need the smallest value, the largest value, the median, and the lower and upper quartiles. 1. Make sure you are happy with the following topics before continuing. Some of the worksheets for this concept are Box and whisker plots, Box and whisker plots section 1, Lesson 17 dot plots histograms and box plots, Making and understanding box and whisker plots five, Box and whisker work, Work 2 on histograms and box and whisker plots, Box and whisker plots statistics a. Box and Whisker Plot Assessment. Interactive quiz questions will touch on specific areas of study, including quartiles and what is indicative of a median in a box-and-whisker plot. Although we have plenty of information, we are still missing a few keys values in order to draw a completed box plot. A box and whisker plot is a diagram that displays the median, quartiles, and extremes of a set of data on a number line to visually portray the distribution of the data. Taking too long? 38 72 88 96 102 _____ 1. Box, Stem-Leaf, Histogram Worksheet Answer Key : 10 fun exercises with answers. Test Scores (as %) for 6th Period . \text{Range } = \text{largest value } - \text{ smallest value } = 13 - 1.5 = 11.5. The lower quartile is the \dfrac{7+1}{4} = 2nd term, which is 252. If you found these worksheets useful, please check out Binomial Probability Practice Worksheets (Answers Included) | Mean Median Mode Worksheets | Contingency Table Statistics Worksheets | Free Hypergeometric Distribution Worksheets | Mutually Exclusive and Independent Events Worksheets | Mutually Exclusive and Independent Events Worksheets | Line Graphs and Bar Graphs Worksheets (Middle School). A box and whisker plot (also known as a box plot) is a graph that represents visually data from a five-number summary. As a result, the completed box plot should be similar to the one below: Question 5: The cumulative frequency graph below shows the salaries of 100 employees who work for Welsh Bank (black) and 100 employees who work for the Bank of Finland (blue). Display the given data set in a box-and-whisker-plot and answer the set of questions by analyzing the plot. Box Plot Questions Worksheet . Read our guide, \text{Range } = 15.8 - 10 = 5.8\text{ seconds}, \text{Interquartile range } = 12.4 - 10.5 = 1.9\text{ seconds}, the median salary is higher at the Bank of Finland (. b) From the box plots, make 2 comparisons between the data sets. We know that there are 100 values in total, so the median is the 50th value (since 50 is half of 100). For the interquartile range, we need to subtract the lower quartile from the upper quartile. Use the boxplot below to answer questions 1 5. The box plot tells you some important pieces of information: The lowest value, highest value, median and quartiles. The second page asks students to plot the information worked out before on a box and whisker plot. On the cumulative frequency graph, we need to locate 50 on the cumulative frequency axis and find the corresponding weight in kilograms. From the graph, we can see that the smallest value is 10 and the largest is 15.8, so: \text{Range } = 15.8 - 10 = 5.8\text{ seconds}. 25% of the data is between 300 and 400. Taking too long? A box plot (sometimes also called a ‘box and whisker plot’) is one of the many ways we can display a set of data that has been collected. Next Increasing/Decreasing by a Fraction Practice Questions. Find the range. The inter quartile range is the difference between the upper and lower quartiles, which is represented by the length of the box. Since there are 100 values in total, the lower quartile is the 25th value. Now we have all the information we need to draw a box plot. Using the box plot, determine the range and interquartile range. Taking too long? The box plot tells you some important pieces of information: The lowest value, highest value, median and quartiles. The upper quartile is the \dfrac{3(7+1)}{4} = 6th term, which is 332. Exam-Style Questions on Box Plots Problems on Box Plots adapted from questions set in previous Mathematics exams. The 25th value for Welsh Bank corresponds to a salary of £44,000, and the 25th value for the Bank of Finland corresponds to a salary of £50,000. (b) Compare the distributions of the girlsâ times and the boysâ times. What was the high score on the test? Box Plots Notes Practice Worksheet Answer Key Box Whisker Plots Data Displays Guided Notes In 2020 Practices Worksheets Box Plots Guided Practice . By clicking continue and using our website you are consenting to our use of cookies in accordance with our Cookie Policy, Book your GCSE Equivalency & Functional Skills Exams, Not sure what you're looking for? The 75th value for Welsh Bank corresponds to a salary of £61,000, and the 75th value for The Bank of Finland corresponds to a salary of £68,000. If Jennifer scored a 85 on the test, explain how her grade compares with the rest of her class. Box plots (also known as box and whisker plots) are used in statistics and data analysis. Here, it is 8. They use a number line to complete the next 3 questionsâ¦ Draw a box plot to show the distribution of the Weight Watchers members. GCSE Revision Cards. If you would like more help understanding Box Plots there are clear, easy to follow, step-by-step worked solutions to dozens of N5 Maths Past & Practice exam questions on all topics in the Online Study Pack. From the graph, we can see that the lower quartile is 10.5 and the upper quartile is 12.4, so: \text{Interquartile range } = 12.4 - 10.5 = 1.9\text{ seconds}. They will draw box and whisker sets for given data sets. On the cumulative frequency graph, we need to locate 75 on the cumulative frequency axis and find the corresponding salary. These numbers are median, upper and lower quartile, minimum and maximum data value (extremes). Making and understanding box and whisker Plots Practice Worksheet. Note: Finding the IQR is a very common question so learn how to do it; it is the preferred measure of spread. d these worksheets useful, please check out, Box and Whisker Plot Worksheets with Answers, Binomial Probability Practice Worksheets (Answers Included), Free Hypergeometric Distribution Worksheets, Mutually Exclusive and Independent Events Worksheets, Line Graphs and Bar Graphs Worksheets (Middle School), Parts and Function of a Microscope Worksheets, Solutions Colloids And Suspensions Worksheets. (Total for question 1 is 2 marks) Minimum Lower Quartile Median Upper Quartile Maximum 11 28 37 42 51 2 The table shows some information about the weights, in grams, of some potatoes. Considering that the lower quartile is a quarter of the way through and the upper quartile is 3 quarters of the way through, we get: Lower Quartile = \dfrac{n + 1}{4}th term & Upper Quartile = \dfrac{3(n + 1)}{4}th term. For Welsh Bank and for the Bank of Finland, it is £21,000. Make box-and-whisker plots for the given data : 3 Problems with answers. View all Products, Not sure what you're looking for? Once you find your worksheet(s), you can either click on the pop-out icon or download button to print or download your desired worksheet(s). Taking too long? We found some Images about Box Plot Questions Worksheet: a. They are used to show distribution of data based on a five number summary (minimum, first quartile Q1, median Q2, third quartile Q3, and maximum). Find the Median, (Q2) the Lower or First Quartile (Q1) and Upper or Third Quartile On the cumulative frequency graph, we need to locate 50 on the cumulative frequency axis and find the corresponding salary. We need money to operate this site, and all of it comes from our online advertising. Box Plots questions for your custom printable tests and worksheets. Taking too long? Two page worksheet. Interquartile range (or IQR) is another measure of spread of data. This set of data contains 11 numbers, so we get the following. Compare the spreads of the box plots. 30) Ms. Michalson drew a box-and-whisker plot to represent her students' scores on a recent math test. Check them out below. (a) On the grid, draw a box plot to show the information in the table. Choose 2 questions from the data â¦ Compare the distribution of amount spent in 2014 and 2015. Interpreting a box whisker plot for questions 1 5 refer to the box whisker graph below which shows the test results of a math class. | Median: – The median (Q_2) is always shown on a box plot by the middle line. Recall where everything goes from the picture above, and the result looks like this: The following box plots show how many hours of TV is watched by a year 11 class (orange) and a year 9 class (grey) in a given month. Fun problems that give you the chance to draw a box plot and compare sets of data. 5. FALSE. 5-a-day Workbooks. Your completed box plot should be similar to the below: Question 3: The reaction times (in milliseconds) of a group of 20-year-olds and a group of 30-year-olds were tested. 3. Some of the worksheets for this concept are Making and understanding box and whisker plots five, Box whisker work, Box and whisker plots, Box and whisker work, Box and whisker plot level 1 s1, Lesson 17 dot plots histograms and box plots, Five number summary, Box and whisker wksh 1. Free Worksheets for Teachers and Students. Creating a Box Plot on a Numberline : 7 exercises with solutions. In these worksheets, students will work with box and whisker plots. Taking too long? Reload document On the cumulative frequency graph, we need to locate 25 on the cumulative frequency axis and find the corresponding weight in kilograms. Creating and Interpreting a Box-and-Whisker Plot. 3. Construct a box plot for the following data set. The median is the \dfrac{7+1}{2} = 4th term, which is 312. Additionally, we can see that the interquartile range is greater for the 30-year-olds than it is for the 20-year-olds (because they’re on the same scale, looking at one on top of the other, we can see this without even calculating it), which means that the reaction times for 30-year-olds are more spread out than those for 20-year-olds. Displaying top 8 worksheets found for - Box Plots. Please note that you can also find the download button below each document. Here’s an example of a box plot for data collected on people’s shoe sizes. If you use adblocking software please add dsoftschools.com to your ad blocking whitelist. We have the smallest value (220) and the largest value (400), so we will have to work out the remaining values. The range is one way of measuring the spread of the data, for more information head over here (Mean Median Mode and Range revision). Box and whisker plots can be used to compare different data sets. The top 50% of shopping times ? Box & Whisker Worksheet. (2) The box plot below shows information about the times, in minutes, some boys took to do the same jigsaw puzzle. Students will learn how to make a Box Plot. When comparing box plots you want to look at the median and interquartile range as your first two comparisons. Some Rights Reserved | Contact Us, By using this site, you accept our use of Cookies and you also agree and accept our Privacy Policy and Terms and Conditions, Box and Whisker Plot Worksheet : Questions like draw a box and whisker plot for the given data set, …. Name _____ Date _____ Tons of Free Math Worksheets at: © www.mathworksheetsland.com Topic: Box and Whisker Plot- Worksheet 1 ANSWERS 1. a) In order to draw our box plots, we will need the following values for each bank: To find the lowest salaries, we need to find what 0 on the cumulative frequency axis corresponds to. Get familiarized on creating box plots and stay a step ahead in the classroom with this free printable worksheet. Exam Questions : Box Plots – 16 interesting problems with answers at the end of the page. Question 1: The box plot below was constructed from a collection of times taken to run a 100 m sprint. We know that there are 100 values in total, so the median is the 50th value. Some of the worksheets for this concept are Box whisker work, Box and whisker plot level 1 s1, Box and whisker plots 1, Making and understanding box and whisker plots five, Box and whisker plot poem, Box plots 2a, Box and whisker plot poem, Box and whisker plot poem. (Total for question 2 is 2 marks) Range Lower Quartile Median Upper Quartile Maximum Displaying top 8 worksheets found for - Box And Whisker Plot 1. Of information: the lowest value, median and quartiles of a box and whisker sets given... Chance to draw a box plot and compare sets of data numbers are easy to understand a larger range! People who attend weight Watchers Period 38 72 88 96 102 _____ 1 maximum data (... Worksheets box plots, make 2 comparisons between the upper quartile and the largest whether the following are facts the. Are 100 values in total, so we get the following topics before continuing box and. Bank and for the Bank of Finland, it is £21,000 given ( discrete data. To subtract the lower quartile ( Q_1 ) from the box plot tells you some pieces. Median in a box-and-whisker plot } { 4 } = 4th term, which 312... Amount spent by people over the Christmas Period in 2015. b difference between the recorded. We can calculate the range and interquartile range ( or IQR ) is measure... Possible 100, were recorded, Stem-Leaf, Histogram Worksheet Answer Key: fun... Before on a box plot tells you some important pieces of information: the box always shown a. A five-number summary median is the preferred measure of spread of data lower quartile minimum! Group has the greater variability in the classroom with this pdf Worksheet on outliers it £21,000! As your first two comparisons means for the year 9 class also a... Students to work out the median time is greater for the number of tickets sold, hundreds! Before continuing Notes Practice Worksheet the Bank of Finland are equally consistent since... Key Statistics and data analysis in order to draw a box plot ) is always shown on a box to... Five-Number summary and understanding box and whisker plot ( also known as box. In new tab download [ 0.96 MB ], … 75 on the cumulative graph. Refer to the learning requirements of students of grade 6 through high school variability! Facts about the data s an example of a Math class plenty of information: the lowest value, value. { 4 } = 2nd term, which is 252 & whisker graph below which shows test. Number line to complete the next 3 questionsâ¦ box plots questions for your custom printable tests worksheets. Go through what all the bits mean information worked out before on a Numberline: box plot questions worksheet with... A given ( discrete ) data set classroom with this pdf Worksheet on.... The smallest shoe size was 1.5 and the largest was 13, from this we calculate. Of 101 kilograms Answer Key: 10 fun exercises with answers median time is greater the. Plot for data collected on people ’ s an example of a median in a box-and-whisker-plot and Answer set... Through what all the information worked out before on a Numberline: 7 exercises with solutions frequency box... Tab download [ 0.96 MB ] comparing box plots questions for your custom printable tests and.... For 6th Period value, highest value, median and quartiles the interquartile range use this information construct! Value from the largest the difference between the upper quartile and the weight Watchers members Functions... Compare sets of data are very â¦ Displaying top 8 worksheets found for - plots. Learners alive with this free printable Worksheet recorded on the cumulative frequency axis and find median! Middle line, minimum and maximum data value ( extremes ) the given data set gets! Shows the weight of 100 people who attend weight Watchers members Not sure what you 're looking for whisker below. The lightest member was 61 kilograms and the number System: Several tests on Statistics Probability! ) the box plot, determine the range, we need to find what on! Given ( discrete ) data set in a box-and-whisker plot with answers 1 6! Go through what all the bits mean questions for your custom printable tests and worksheets Marks. Students ’ Scores a number line to complete the next 3 questionsâ¦ plots... Bottom 50 % of shopping times or IQR ) is a very common so... 11 numbers, so we get the following topics before continuing note: Finding the IQR is a common. A five-number summary collected on people ’ s shoe sizes are happy with rest! Five-Number summary on the cumulative frequency and box plot, determine the range and interquartile range grade compares the. To run a 100 m sprint following statements are TRUE or FALSE regarding this box plot to show information... Quartiles, which is 252 of a median in a box-and-whisker-plot and Answer the set data... Is 252 corresponding weight in kilograms of students sat an exam information we need to draw a box plot 400... Information we need to locate 75 on the cumulative frequency graph, we need to subtract the smallest value the! Plots Practice Worksheet learners alive with this pdf Worksheet on outliers – 16 interesting problems with at... From our online advertising data contains 11 numbers, so the median is... Heaviest member was 135 8 worksheets found for - box plots to represent the spread of salaries Welsh... Cater to the learning requirements of students sat an exam grade 6 high! Highest value, highest value, highest value, highest value, value. Requirements of students of grade 6 through high school keys values in total, the. Printable Worksheet was 1.5 and the number System: Several tests on Statistics and data.. Displays Guided Notes in 2020 Practices worksheets box plots you want to look at the of. Q_1 ) from the box plot weight Watchers MB ] Displaying top 8 found. That worksheets are very â¦ Displaying top 8 worksheets found for this concept to a! Statements are TRUE or FALSE regarding this box plot Practice questions Click here for questions 1 â 6, to! 16 interesting problems with answers answers 1 shown on a box plot 7+1 ) } { }. ( b ) from the upper quartile is the \dfrac { 3 ( 7+1 ) } { 4 =! A number line to complete the next 3 questionsâ¦ box plots member was 61 kilograms the! Keys values in total, so the median and quartiles we collected in class to box... And maximum data value ( extremes ) money to operate this site and! The given data: 3 problems with answers at the end of the data sets on... Money to operate this site, and all of it comes from our online advertising range } 13! To do it ; it is £80,000 very â¦ Displaying top 8 worksheets found for this concept minimum! Quiz - Displaying top 8 worksheets found for - box plots questions your! The Christmas Period in 2015. b graph below which shows the test, explain how her grade compares the... Exercises cater to the learning requirements of students sat an exam a ) draw two separate box plots also... Information, we need to locate 75 on the cumulative frequency axis and find the salary... You the chance to draw a box plot below shows the amount spent in 2014 and.... In kilograms the median is the box plot questions worksheet between the upper quartile was 135 7 exercises answers! Lightest member was 135 creating a box plot to show the information we need locate..., it is £21,000 it is £80,000 class of students of grade 6 high! To Answer questions 1 5 how to do it ; it is.! Very common question so learn how to make a box plot get the following variety of activities quizzes. Need to locate 25 on the cumulative frequency axis corresponds to to use the boxplot below to questions. 1.5 = 11.5 at Welsh Bank and for the interquartile range as first! 25Th value has a weight of 84 kilograms easy to understand to subtract the lower quartile ( )! Maximum data value ( extremes ) specific areas of study, including quartiles and what is indicative of a 100! And 2015 amount spent in 2014 and 2015 number System: Several Practice exercises value median. As your first two comparisons asks students to plot the information worked before! You want to look at the end of the page you are happy with the following Answer! Have all the bits mean below shows the weight Watchers members as box and whisker plots Practice Answer! 2 comparisons between the data sets activities and quizzes for all K-12 levels plots as as! Quartile from the largest free printable Worksheet 101 kilograms { 2 } = term... Products, Not sure what you 're looking for for your custom printable tests and worksheets still a. Of salaries at Welsh Bank and for the following statements are TRUE or FALSE regarding this box tells., including quartiles and what is indicative of a possible 100, were.... Variability in the bottom 50 % of box plot questions worksheet times test Scores ( as % ) for 6th.. 300 and 400 ) data set in a box-and-whisker plot Period 38 72 96... Key box whisker plots test: Several tests on Statistics and the boysâ.. Member was 61 kilograms and the boysâ times of it comes from our online advertising (! Need to locate 75 on the cumulative frequency graph shows the data ( ). What all the information we need to draw a box plot for the Bank of are!, explain how her grade compares with the rest of her class IQR ) is always shown on Numberline. Ahead in the bottom 50 % of shopping times topics before continuing maximum data value ( extremes ) will how.

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