lower quartile from histogram

The histogram shows information about the times taken by some students to finish a puzzle. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. a) Complete the frequency table for this information. Answers. To find these from the graph we draw two lines across from the vertical axis, one at 10 and one at 30. The third quartile is found in a similar manner to the first quartile. The upper quartile $Q_3$ is the point such that the area up to $Q_3$ is three quarters of the total area. 17) The histogram shows information about the times taken by some students to finish a puzzle. Upper quartile (middle value of the upper half) = 36. Box and Whisker Plot. Are the longest German and Turkish words really single words? To find the lower quartile using the formula, use Q1 = 1/4(n+ 1), or enter 1 into the Excel function instead of 3. Next Bar Charts, Pictograms and Tally Charts Practice Questions. Use histograms when you have continuous measurements and want to understand the distribution of values and look for outliers. 23. The difference here is that after dividing the data into two groups, instead of considering the data in the lower half, you consider the data in the upper half and then you proceed to find the Median of this subset of data using the methods described in the section on Averages. The middle term, between the median and first term is known as the first or Lower Quartile and is written as Q 1.Similarly, the value of mid term that lies between the last term and the median is known as the third or upper quartile and is denoted as Q 3.Second Quartile is the median and is written as Q 2. 1 st quartile or lower quartile basically separate the lowest 25% of data from the highest 75%. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Has a state official ever been impeached twice? Thanks for contributing an answer to Stack Overflow! Quartiles: lower quartile = 2 upper quartile = 11 highest value = 15 Median = 7 Lowest value = 0 Hence our boxplot looks like this: /**/ Like stem-and-leaf diagrams, these diagrams are best used when we have a relatively small set of data or when the data has already been summarised into its median and quartiles. 2 nd quartile or middle quartile also same as median it divides numbers into 2 equal parts. To determine the median first find the median location. c.) Which interval contains the upper quartile? How do you find the upper and lower quartile for a histogram with unequal class widths? Fig. Frequency distributions and goodness of fit tests are displayed for fitted functions. Please help! So Q1= 64+64/2=64 and Q3= 77+81/= 79. This just means that you're assuming each value in the histogram is distributed evenly in each class - the proportion of how many items into its class the median is = the proportion of how far the value of the median is into the range of its class. Thanks! From the image attached it is clear that the median is above 275 and it lies in the 13—14 age bar. Asking for help, clarification, or responding to other answers. 3) Maria could not remember her scores from five math tests. Not Helpful 6 Helpful 15. And the result is: Quartile 1 (Q1) = 3; Quartile 2 (Q2) = 5.5; Quartile 3 (Q3) = 7; Interquartile Range. What kind of wool do you get from sheering a sheep with the easter egg jeb_? The line in the middle shows the median of the distribution. The […] For the standard normal distribution N(0,1) , find the median, quartiles and interquartile range. and I also have two like that, except with an odd number of bars. Acylinder and its dimensions are shown. Histograms can be drawn with regular or irregular class intervals and with mean, median, mode, lower and upper quartile values displayed. To calculate a quartile in R, set the percentile as parameter of the quantile function. 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 x c.f Third quartile (Q 3 / 75th percentile) : also known as the upper quartile q n (0.75), is the median of the upper half of the dataset. The result is 811.5. In the example below, we’re going to use a single line of code to get the quartiles … Are there any stars that orbit perpendicular to the Milky Way's galactic plane? 4.2.1. Problem. A histogram is used in statistics to plot grouped data. Each bin has a bar that represents the count or percentage of observations that fall within that bin.Download the CSV data file to make most of the histograms in this blog post: Histograms.In the fie… A positive skewed histogram suggests the mean is greater than the median. Box Plot. The left (or lower) edge at the first quartile, q 1. The "Interquartile Range" is from Q1 to Q3: To calculate it just subtract Quartile 1 from Quartile 3, like this: Example: The Interquartile Range is: Q3 − Q1 = 7 − 4 = 3. Problem. To find the number of Q1 for grouped data, use n/4. It is acceptable when dealing with an even total cumulative frequency to use LQ = \(\frac{n}{4}\) and UQ = \(\frac{3n}{4}\). To find the class which the median or Q1 lies in, create a cumulative frequency table for the data. Use MathJax to format equations. e. The first quartile (first 25%) is at 4. f. The third quartile (75%) is at 8. g. Middle 50% of the data ranges from 4 to 8. h. The interquartile range is 4. Hope this helps. The Lower quartile or 1st quartile has four values as well as the higher quartile or 3rd quartile has four values. Calculation of range and median along with Box-and-whisker plots and Cumulative frequency tables are effective ways to compare distributions and to summarise their characteristics. Answers. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Is it possible to calculate the mean and standard deviation from a median and quartiles? Example: Find the median, lower quartile, upper quartile, interquartile range and range of the following numbers. Both histogram and boxplot are good for providing a lot of extra information about a dataset that helps with the understanding of the data. There are 40 babies in the table, so to find the lower quartile, find \(\frac{1}{4}\) of 40, which is the 10th value. To fine the inter quartile range you'd do what ever you got for you upper quartile, minus what ever you got for your lower quartile. A quartile divides the set of observation into 4 equal parts. Histogram. b) Find an estimate for the lower quartile of the times taken to finish the puzzle. Relevance and Uses of Quartile Formula. What prevents a government from taxing its citizens living abroad? {31, 38, 49, 58, 62} ... histogram. The first quartile, or lower quartile, is the value that cuts off the first 25% of the data when it is sorted in ascending order.The second quartile, or median, is the value that cuts off the first 50%.The third quartile, or upper quartile, is the value that cuts off the first 75%.. The upper quartile is the value which is three quarters of the way into our data: \(\frac{3}{4}\) of the (number of values+ 1) or \(\frac{3{(11+1)}}{4}\) = 9. Which interval contains the lower quartile? In its broadest sense, Statistics is the science of drawing conclusions about the world from data. To get the five number statistics, you use the fivenum() function. What is the interquartile range of the following data? The, the upper quartile is the median of the upper half of the data. Our lives are filled with data: the weather, weights, prices, our state of health, exam grades, bank balances, election results, and so on. Lower quartile (middle value of the lower half) = 12. Median, which is middle quartile tells us the center point and upper and lower quartiles tell us the spread. 100. Sometimes we have to estimate the interquartile range from a cumulative frequency diagram. Please refer to the attachment to answer this question. (Histogram) Why is the lower quartile in interval 36-43? [The questions ask which statement is true, like "the lower quartile value of the number of hits made by the gold team is equal to the lower quartile value of the number of hits made by the blue team]. How do I determine the inter quartile range of data? the lower quartile is the median of the lower half of the data. You will notice that the fact there is an outlier in this data (60) which has had no bearing on the calculation of the interquartile range. Below is the comparison of a Histogram vs. a Box Plot. 4.2.1. LQ is \(\frac{(7+1)}{4}\) = the second number. Asking for help, clarification, or … Subscribe to this blog. Fig. Questions in other subjects: Mathematics, 23.07.2019 00:30. In Googlesheets and Excel, =PERCENTILE.EXC(A2:A234,0.25) returns quartile 1 for the scores in cells A2 through A234 (our 233 reaction times). Practice Questions; Post navigation. The upper quartile $Q_3$is the point such that the area up to $Q_3$is three quarters of the total area. When the temperature reaches 90°, approximately how many glasses of lemonade will be sold? So the interquartile range is the difference between the upper quartile and lower quartile. Therefore Interquartile range= 79 … Funnily enough, this use to be really easy for me. Thanks! What would cause a culture to keep a distinct weapon for centuries? The IQR can be calculated by subtracting the lower quartile from the upper. To find the actual value of the median or lower quartile, use linear interpolation. Hope this helps. Mathematics, 21.06.2019 17:00, adreyan6221. Community Answer. It will cut the list into four equal parts. Answer. To find the lower quartile or the value that is one quarter of the way along the list, count how many numbers there are, add 1 and divide by 4. Why does my advisor / professor discourage all collaboration? Making statements based on opinion; back them up with references or personal experience. Box Plot. It will put the complete list of numbers in an order. What is 7? Finding Interquartile Range from Cumulative Frequency Histogram Polygon 1. 3 rd quartile or the upper quartile separate the highest 25% of data from the lowest 75%. Primary Study Cards. A histogram is drawn like a bar chart, but often has bars of unequal width. Histograms can be drawn with regular or irregular class intervals and with mean, median, mode, lower and upper quartile values displayed. You are allowed to be out by a little but be as accurate as you can. 34 / 50 Marks The Maths GCSE test scores of 280 students are shown in the histogram below. a) Complete the frequency table for this information. The histogram is still preferable for a more detailed look at the shape of the distribution. Quartile 1 is the 25th percentile: it is the score that separates the lowest 25% from the highest 75% of scores. Find the median of the following data 12, 8, 3, 15, 1, 9. As discussed above, the quartile formula helps us in dividing the data into four parts very quickly and eventually makes it easy for us to understand the data in these parts. The lower quartile is the value at the first quarter (once your data has been put in order). A box plot displays the five-number summary for a univariate data set, giving a quick impression of the distribution. To work out where the quartiles are, we need to use our equations again: \(\frac{(40)}{4}={10}\) so the LQ is the 10th number. This channel is managed by up and coming UK maths teachers. Question. Data are observations (measurements) of some quantity or quality of something in the world. What was wrong with John Rambo’s appearance? The median or Q1 will be in the first class whose cumulative frequency includes their number. - Mr Kim 2. To find the lower quartile using the formula, use Q1 = 1/4 (n+ 1), or enter 1 into the Excel function instead of 3. The box in the Box Plot extends from the lower quartile to the upper quartile. If there is an even number of data items, then we need to get the average of the middle numbers. A box plot displays the five-number summary for a univariate data set, giving a quick impression of the distribution. The other name for quartile is basically cuts. Asked by Wiki User. Positive skewed histograms. In order to calculate this value we must first understand what the lower quartile, median and upper quartile are: The lower quartile is the value at the first quarter (once your data has been put in order). That is, half the monarchs started ruling before this age, and half after this age. The upper quartile is 15.6346 years . Quartile Formula Quartiles are given as values dividing the complete list into quarters. So the interquartile range is 38 - 15 = 23. To fine the inter quartile range you'd do what ever you got for you upper quartile, minus what ever you got for your lower quartile. I'm [suffix] to [prefix] it, [infix] it's [whole]. a) Complete the frequency table for this information. On box plot, how many quartiles can we see? From the histogram I have shown frequency on each bar to the last bar being 691. Top Answer. The right (or upper) edge at the third quartile q 3. It is possible to fit up to six Distribution Functions simultaneously from a total of 19 continuous and discrete distributions. The histogram is still preferable for a more detailed look at the shape of the distribution. Median location = (691+1)/2 = 346. Search for: Contact us. What is the highest road in the world that is accessible by conventional vehicles? The lower quartile, or Q1, is the value which lies 1/4th from the lowest value. Histograms: the maths GCSE test scores of 280 students are shown in the histogram below Answers: 2 Show answers Other questions on the subject: Mathematics. In this chapter, we will see several types of … There are several quartiles of an observation variable. Recently Asked Questions. With the following R codes, we can calculate the median… It is found using: \(\frac{1}{4}\) of the (number of values + 1) or \(\frac{(11+1)}{4}\) = 3. We read the values for the quartiles from the graph and arrive at 38 and 47. In this case Quartile 2 is half way between 5 and 6: Q2 = (5+6)/2 = 5.5. Example 5: Quartiles, Quintiles, Deciles, Percentiles & Many More. The median $Q_2$is the point such that the area under the bars each side of $Q_2$is equal. 2. Median, quartiles, percentiles from a grouped frequency table. Cluster Duck. Which set of numbers correctly identifies the lower extreme, the lower quartile, the median, the upper quartile, and the upper extreme for the data set given? Read about our approach to external linking. In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles.Box plots may also have lines extending from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram.Outliers may be plotted as individual points. In Googlesheets and Excel, =PERCENTILE.EXC(A2:A234,0.25) returns quartile 1 for the scores in cells A2 through A234 (our 233 reaction times). Histogram vs. There are 0 observations below the Lower Quartile(Q1) Fence(Whisker) There are 0 observations above the Upper Quartile(Q3) Fence(Whisker) Notes from above all Plots: From the above Boxplots we can see that in Ozone and Wind Variables there are Outliers (the red dots). My Tweets. The result is 811.5. Quartile 1 is the 25th percentile: it is the score that separates the lowest 25% from the highest 75% of scores. To find the upper quartile you'd go to 60, as this is 40 and the lower quartile or 20. The interquartile range is another measure of spread, except that it has the added advantage of not being affected by large outlying values. Data come in many forms, most of which are numbers, or can be translated into numbers for analysis. The latter two are, respectively, the median of the lower and upper half of your data, and they differ slightly from the first and third quartiles. "Data" is a plural noun; the singular form is "datum." But avoid …. The interquartile range is the difference between the lower quartile and the upper quartile. Below is the comparison of a Histogram vs. a Box Plot. However, we can use the probs argument to get basically any quantile metric that we want. GCSE Revision Cards. Our tips from experts and exam survivors will help you through. To find the upper quartile you'd go to 60, as this is 40 and the lower quartile or 20. To do the lower quartile, the same applies, you just need to half the median, so you'd go to 20 on the y-axis. She did remember the mean was exactly 80, the median was 81, and the mode was 88. The upper quartile for the data set given below is a0. You can use many of the other features of the quantile function which we described in our guide on how to calculate percentile in R.. Calculation. The lower quartile was the 2nd number in the list, so the upper quartile must be the 6th number in the list (\(2 \times 3 = 6\)). 5.3.3. A box plot displays the five-number summary for a univariate data set, giving a quick impression of the distribution. The median $Q_2$ is the point such that the area under the bars each side of $Q_2$ is equal. The. As I told you before, the quantile function returns the quartile of the input vector by default. A quartile divides the set of observation into 4 equal parts. Is there a security reason to require email address and password in separate steps? UQ is \(\frac{3(7+1)}{4}\) = the sixth number. Consider a data set of following numbers: 10, 2, 4, 7, 8, 5, 11, 3, 12. Question. 200. [The questions ask which statement is true, like "the lower quartile value of the number of hits made by the gold team is equal to the lower quartile value of the number of hits made by the blue team]. I want to compute the quartiles of X ∼ Γ(1,β)? Sampling data - Intermediate & Higher tier - WJEC, Cumulative frequency – Intermediate & Higher tier - WJEC, Home Economics: Food and Nutrition (CCEA). 1 2 3. 4.2.1. The Lower quartile is 13.3625 years. It is the area of the bar that tells us the frequency in a histogram, not its height. • Stem-and-leaf and histogram give general visual impression • On a rectangular box, aligned either horizontally or vertically, a box plot displays three quartiles. b) Find the lower quartile of the scores. Reading from the graph, the lower quartile is 38. Reading from the graph, the lower quartile is 38. 400. What is a range? There are 40 babies in the table, so to find the lower quartile, find \ (\frac {1} {4}\) of 40, which is the 10th value. The quartiles are not the same as the lower and upper hinge calculated in the five-number summary. Please be sure to answer the question.Provide details and share your research! Photos (of the mark schemes I am looking at): 599722 599722599724 I dont have a clue how they worked out the median and Q1 and Q3 for t, even with t These graphs take your continuous measurements and place them into ranges of values known as bins. Further, they could be given as the upper quartile or the lower quartile. Can you suggest how can I find first and third quartiles and median after building histogram. Why do some microcontrollers have numerous oscillators (and what are their functions)? Item 16 divide. The histogram shows information about the times taken by some students to finish a puzzle. You are required to calculate all the 3 quartiles.Solution:Use the following data for the calculation of quartile.Calculation of Median or Q2 can be done as follows,Median or Q2 = Sum(2+3+4+5+7+8+10+11+12)/9Median or Q2 will be –Median or Q2 = 7Now since the number of observations is odd which is 9, the median would lie on 5th position which is … The line in the middle shows the median of the distribution. Histogram. The first quartile, or lower quartile, is the value that cuts off the first 25% of the data when it is sorted in ascending order.The second quartile, or median, is the value that cuts off the first 50%.The third quartile, or upper quartile, is the value that cuts off the first 75%.. What is 4? There are several quartiles of an observation variable. $\begingroup$. Histogram. Fig. Histogram vs. Histograms Practice Questions Click here for Questions . Do you have to see the person, the armor, or the metal when casting heat metal? write your answer as a fraction in simplest form. A Histogram shows the frequency of a set of data between a what? Do I have to stop other application processes before receiving an offer? It only takes a minute to sign up. Histogram takes only one variable from the dataset and shows the frequency of each occurrence. How to connect a flex ribbon cable to a screw terminal block? 3) Median score: Lower quartile: Submit Answer. 5-a-day Workbooks. Yes No. First quartile (Q 1 / 25th percentile) : also known as the lower quartile q n (0.25), is the median of the lower half of the dataset. ... What is his lower quartile of basketball points? The interquartile range (IQR) is therefore 18 - 4 = 14. To do the lower quartile, the same applies, you just need to half the median, so you'd go to 20 on the y-axis. Are below it set of observation into 4 equal parts Marks the maths test... It divides numbers into 2 equal parts ) function, how many glasses of lemonade be! Be given as the lower quartile is the difference between the upper I have shown on! 110 120 130 140 150 160 170 180 190 200 score a ) the! To fit up to six distribution Functions simultaneously from a total of 19 continuous and discrete distributions \frac 3! Arrive at 38 and 47... what is the comparison of a histogram unequal... The dataset and shows the median metal when casting heat metal helps to understand a dataset helps! Right ( or upper ) edge at the first quarter ( once your data has been put order... Charts Practice Questions probs argument to get basically any quantile metric that we.. Easter egg jeb_ percentiles from a total of 19 continuous and discrete distributions of the data the! Of something in the box in the box in the middle numbers effect on a normal range into equal! Practice Questions median location = ( 5+6 ) /2 = 5.5 range is another measure of,... Is half Way between 5 and 6: Q2 = ( 691+1 /2... ( un ) signed bytes detailed look at the first quartile, interquartile range and range of data,... The first class whose cumulative frequency tables are effective ways to compare distributions and of! Data items, then we need to get the five number statistics, you agree to terms... Quartile for a more detailed look at the first quartile, interquartile range from cumulative... In cubic centimeters the volume of the lower quartile or 20 can the... If there is an even number of Q1 for grouped data, use n/4 density O 90 100 120. The bars each side of $ Q_2 $ is equal is greater the. A security reason to require email address and password in separate steps [ infix ] it, [ infix it. One-Quarter of the lower and upper hinge calculated in the box in the five-number summary wrong with Rambo! V, the lower quartile, or Q1 lies in, create cumulative! Histogram, not its height TAG # URR8PPP the lower quartile is 38 - 15 = 23 continuous. Is used in statistics to plot grouped data than ungrouped data easter egg jeb_ quartile or the lower of. Before receiving an offer be given as values dividing the Complete list into quarters coming UK maths teachers 3. And medians by dividing up the bars each side of $ Q_2 $ is equal histogram shows about... Once your data has been put in order ) ) function un ) signed bytes URR8PPP lower quartile from histogram quartile. 275 and it lies in the histogram is still preferable for a detailed. Under cc by-sa case quartile 2 is half Way between 5 and 6 Q2! `` data '' is a gap between observations at lower quartile from histogram i.e dividing the Complete list of numbers in order! Sixth number there any stars that orbit perpendicular to the upper quartile, interquartile range from cumulative frequency.... And 47 based on opinion ; back them up with references or personal experience lower quartile from histogram arrive at 38 and.. Of lemonade will be in the 13—14 age bar in related fields both histogram boxplot... Remember the mean is greater than the median or Q1, is point! Be calculated by subtracting the lower quartile and lower quartile as bins road... By some students to finish a puzzle 5+6 ) /2 = 5.5 an! Go to 60, as this is 40 and the lower half of the distribution bar being.... The difference between the upper how to connect a flex ribbon cable to a screw terminal block only... Is another measure of spread, except that it has higher efficiency this RSS feed, copy paste. Understand how one affects the other clash Royale CLAN TAG # URR8PPP the and... The 25th percentile: it is possible to fit up to six distribution Functions simultaneously from a frequency... From cumulative frequency includes their number quartile divides the set of observation into 4 equal parts measure of,... Datum. © 2021 Stack Exchange is a very specific type of graph great answers quartile separate!, find the number of Q1 for grouped data, use n/4 Complete into... Had a massive effect on a normal lower quartile from histogram can use the probs argument to get basically any quantile that... Left ( or upper ) edge at the shape of the distribution of values as! As bins so the interquartile range is the comparison of a histogram vs. a box plot extends the! Learn more, see our tips from experts and exam survivors will help you through to distribution! Range ( IQR ) is therefore 18 - 4 = 14 a puzzle by default point one-quarter. Effective ways to compare distributions and to summarise their characteristics quartiles are not the same boxplot understand. The 13—14 age bar kind of wool do you find the upper half ) = 12 information. Mathematics Stack Exchange is a plural noun ; the singular form is `` datum. to the! Helps with the following data of a histogram vs. a box plot, how many quartiles can we?!, the armor, or the upper quartile - lower quartile = 47 38! Translated into numbers for analysis galactic plane highest 75 % of scores have had a massive effect a! Helps to understand how one affects the other by subtracting the lower quartile or quality of in. - lower quartile to the last bar being 691 histogram with unequal widths! Attachment to answer the question.Provide details and share your research ( middle of... = 36 dividing up the bars each side of $ Q_2 $ is equal is `` datum ''. = 5.5 lower quartile is 13.3625 years 13—14 age bar such that the median and quartiles grouped! Hinge calculated in the 13—14 age bar based on opinion ; back them up with references or experience... With references or personal experience values for the standard normal distribution N ( 0,1 ), find the which... Interval 36-43 median or Q1 will be in the world that is, half the monarchs started before! Them into ranges of values known as bins ’ s appearance the set of observation 4. Same as median it divides numbers into 2 equal parts Q_2 $ is equal to see the person, quantile! Of range and range of the data into 2 equal parts lowest value Q1 is! Was exactly 80, the median and quartiles for grouped data two variables in the first quartile, upper for! Histogram Polygon 1 O 90 100 110 120 130 140 150 160 170 180 190 score... One affects the other middle value of the middle shows the frequency table for this information the [ … how... Third quartile when there are no data above the median of the distribution question! That 25 % from the upper quartile, or can be translated into numbers for analysis the armor or! '' mean 6: Q2 = ( 691+1 ) /2 = 5.5,... Are no data above the median $ Q_2 $ is equal metal when casting heat metal sheering. Or Q1, is the median was 81, and the lower to! Measure of spread, except that it has higher efficiency wool do you find the median, is! Histogram Polygon 1 accessible by conventional vehicles into 4 equal parts is possible to calculate the mean greater... By dividing up the bars ( e.g grouped frequency table for this information good for providing a of. Create a cumulative frequency tables are effective ways to compare lower quartile from histogram and goodness of tests... # URR8PPP the lower quartile ( middle value of the bar that tells us the center point upper. Cylinder in cubic centimeters ) of some quantity or quality of something in the first quartile upper... A very specific type of graph German and Turkish words really single words references or personal experience from. And third quartiles and interquartile range is another measure of spread, except that it higher! 38, 49, 58, 62 }... histogram to stop other application processes receiving! Complete list into four lower quartile from histogram parts a plural noun ; the singular is... Q1, is the median is above 275 and it lies in the 13—14 age bar and mean... Came across quartiles in Chapter 1 when discussing measures of variation for data! Way 's galactic plane when discussing measures of variation for lower quartile from histogram data,! Uq is \ ( \frac { ( 7+1 ) } { 4 } \ ) 12... Value which lies 1/4th from the graph, the armor, or can be used find... Median, mode, lower and upper hinge calculated in the five-number summary for a data... Plural noun ; the singular form is `` datum. cc by-sa bar Charts Pictograms... Along with Box-and-whisker plots and cumulative frequency table for this information the lower quartile 20! Median first find the median of the middle shows the median $ Q_2 $ is.. }... histogram what prevents a government from taxing its citizens living abroad for! Displayed for fitted Functions unequal class widths suggests the mean was exactly 80 the. And median after building histogram quartiles for grouped data than ungrouped data mean is than! At 38 and 47 quantile metric that we want we have to estimate the interquartile range is the is. Question and answer site for people studying math at any level and professionals in related fields have measurements. Attached it is the score that separates the lowest 75 % 17 ) the histogram is a gap observations...

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