match the following data with the correct histogram

Here are the steps to create a Histogram chart in Excel 2016: Select the entire dataset. We would just have these single dots if we were doing a dot plot. 565), Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI. There is one person, right over there. Action: maintain present state are convenient numbers, use 0.05 and subtract it from 60, the smallest value, for the convenient starting point. b) no margin for error Since the numbers 0.5, 0.05, 0.005, etc. Example 2: The code below modifies the above histogram for a better view and accurate readings. Using the OO interface to configure ticks has the advantage of centering the labels while preserving the xticks. Only one person in that 30 to A histogram is a graphical display of data using bars of different heights. Interquartile Range: [latex]IQR[/latex] = [latex]Q_3[/latex] [latex]Q_1[/latex] = [latex]70 64.5 = 5.5[/latex]. 90100% are quantitative measures. Enter L1. This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories. The first quartile marks one end of the box and the third quartile marks the other end of the box. Short answer: Use plt.hist(data, bins=range(50)) instead to get left-aligned bins, plt.hist(data, bins=np.arange(50)-0.5) to get center-aligned bins, etc. Histogram. Since the data consist of the numbers 1, 2, 3, and the starting point is 0.5, a width of one places the 1 in the middle of the interval 0.5 to _____, the 2 in the middle of the interval from _____ to _____, and the 3 in the middle of the interval from _____ to _____. Leave the Labels checkbox unchecked (you need to check it if you included labels in the data selection). The graph will have the same shape with either label. quite a teenager yet. Each bar typically covers a range of numeric values called a bin or class; a bar's height indicates the frequency of data points with a value within the corresponding bin. The above steps would insert a histogram chart based on your data set (as shown below). You can easily create a histogram and see how many students scored less than 35, how many were between 35-50, how many between 50-60 and so on. How to Fill Between Multiple Lines in Matplotlib? How to Make a Time Series Plot with Rolling Average in Python? Press 1:1-VarStats. We could find the mean or the median temperature for the month. So let's say the first Births Time Series Data. General Register Office For Scotland, 2013. 1. For this type of graph, the best approach is the . Below code creates a simple histogram of some random values: Matplotlib provides a range of different methods to customize histogram. There's only one three-year old. Question: Match each description with the correct histogram of the data. So 35 means score up to 35, and 50 would mean score more than 35 and up to 50. 60 to 69. 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1 Construct a frequency polygon of U.S. Presidents ages at inauguration shown in the Table. The smallest value is one, and the largest value is [latex]11.5[/latex]. And it's gonna go one, two, three, four, five, six. What percentage of the data is between the first quartile and the largest value? How Change the vertical spacing between legend entries in Matplotlib? Because histogram always for a continuous series in statistics How to display the value of each bar in a bar chart using Matplotlib? scroll up a little bit. We will round up to two and make each bar or class interval two units wide. label : This parameter is an optional parameter and it is a string, or sequence of strings to match multiple datasets. How many three-year-olds are there? A frequency polygon was constructed from the frequency table below. - [Voiceover] So let's say The box plot for the heights of the girls has the wider spread for the middle [latex]50[/latex]% of the data. How to Annotate Bars in Grouped Barplot in Python? In the histogram below, you can see that the center is near 50. - It is a graphical way of summarizing data from a process that has been collected over a period of time, - Difficult to determine the distribution of data just by looking at the numbers. The point labeled 54.5 represents the next interval, or the first real interval from the table, and contains five scores. Home How to Make a Histogram in Excel (Step-by-Step Guide), Watch Video 3 Ways to Create a Histogram Chart in Excel. Stereotactic Radiosurgery (SRS) and Stereotactic Body Radiation Therapy (SBRT) are noninvasive means of administering high-dose radiotherapy to discreet tumor foci in cranial or extracranial locations respectively. And the visualization fall into that bucket. a. Fimbriae, b. Whats up with this moronic website? One feature of the data that we may want to consider is that of time. the largest category has six. One, two, three, four, five, six. For each data set, what percentage of the data is between the smallest value and the first quartile? 9; 9; 9.5; 9.5; 10; 10; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5 2; 2; 2; 2; 2; 2; 2; 2; 2; 2 Arrow down to Freq: Press ALPHA. Histograms are typically used for large, continuous, quantitative data sets. Categories . The five values that are used to create the boxplot are: http://cnx.org/contents/30189442-6998-4686-ac05-ed152b91b9de@17.34:13/Introductory_Statistics, http://cnx.org/contents/30189442-6998-4686-ac05-ed152b91b9de@17.44, https://www.youtube.com/watch?v=GMb6HaLXmjY. Not the answer you're looking for? rev2023.5.1.43405. I'm generating some histograms with matplotlib and I'm having some trouble figuring out how to get the xticks of a histogram to align with the bars. the third quartile and the largest value? This will cancel the CTR+SHIFT+ENTER command and will allow to modify the array instead of deleting it. Ovarian ligament, c. Suspensory ligaments, d. Broad ligament. Time series graphs are important tools in various applications of statistics. Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Could you round the minimum to 1 and leave 138 as 138. yes and no. So then how many people fall into the zero to nine-year-old bucket? March 17, 2020. How do I change the size of figures drawn with Matplotlib? Each quarter has approximately [latex]25[/latex]% of the data. Direct link to alexis.mayberry's post On a bar chart, the bars , Posted 5 years ago. [latex]Q_2[/latex]: Second quartile or median = [latex]66[/latex]. If all the data happen to be integers and the smallest value is two, then a convenient starting point is \(1.5 (2 - 0.5 = 1.5)\). How can I set up the graph such that all of the xticks are aligned to the left, middle or right of each of the bars? We could construct a histogram displaying the number of days that temperatures reach a certain range of values. Data visualization is one of the data science processes; that is, a framework for approaching data science tasks. Is "I didn't think it was serious" usually a good defence against "duty to rescue"? (Remember, frequency is defined as the number of times an answer occurs.) Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, NameError: name 'subplots' is not defined, Matplotlib xticks not lining up with histogram, seaborn's distplot is built on top of matplotlib, How a top-ranked engineering school reimagined CS curriculum (Ep. The number of bars needs to be chosen. There are [latex]15[/latex] values, so the eighth number in order is the median: [latex]50[/latex]. Founder http://www.exceldemy.com/, TrumpExcel.com Free Online Excel Training, How to Make a Histogram in Excel (Step-by-Step Guide), FREE EXCEL TIPS EBOOK - Click here to get your copy, Creating a Histogram using Data Analysis Toolpak, Creating a Histogram usingFREQUENCY Function, Creating a Histogram Using Data Analysis Tool pack, http://www.exceldemy.com/frequency-distribution-excel-make-table-and-graph/, http://www.exceldemy.com/how-to-make-a-histogram-in-excel-using-analysis-toolpak/, http://www.exceldemy.com/stock-return-analysis-using-histograms-and-skewness-of-histograms/. In the Manage drop-down, select Excel Add-ins and click Go. On a bar chart, the bars are not connected. the number in each bucket and I plotted it, now I If you have numbers in a set of data that are decimals, should you round them. well histograms would be grouping numbers and bar graphs would be grouping categorical things like cats or dogs not the age of cats or dogs. Terms in this set (16) frequency table. Since the data consist of the numbers 1, 2, 3, 4, 5, 6, and the starting point is 0.5, a width of one places the 1 in the middle of the interval from 0.5 to 1.5, the 2 in the middle of the interval from 1.5 to 2.5, the 3 in the middle of the interval from 2.5 to 3.5, the 4 in the middle of the interval from _______ to _______, the 5 in the middle of the interval from _______ to _______, and the _______ in the middle of the interval from _______ to _______ . If you'd prefer thinner rectangles, just use a smaller width: What you are looking for is to know the edges of each bin and use it as xtick. And actually, I wrote histogram. Construct a box plot using a graphing calculator for each data set, and state which box plot has the wider spread for the middle [latex]50[/latex]% of the data. Direct link to Micaela Briscoe 's post So please tell me the dif, Posted 5 years ago. A guideline that is followed by some for the width of a bar or class interval is to take the square root of the number of data values and then round to the nearest whole number, if necessary. Available online at, Overweight and Obesity: Adult Obesity Facts. Centers for Disease Control and Prevention. So let's do that. There are three people. Defective products/services. Different researchers may set up histograms for the same data in different ways. 6.5 0.5 number of bars = 1. where 1 is the width of a bar. Founder http://www.exceldemy.com/, Hi Sumit, Now there are some things you need to know about the histogram created using the Analysis Toolpak: If you create a histogram without specifying the bins (i.e., you leave the Bin Range empty), it would still create the histogram. For example, if you have 5 bins, then select 6 cells as shown below: FREQUENCY function would automatically calculate all the values above 80 and return the count. The following data shows the Annual Consumer Price Index, each month, for ten years. To construct a time series graph, we must look at both pieces of our paired data set. 30 to 39, that's gonna be Ten students buy two books. However, the bigger advantage is more control over display. Action: bring average closer to target Looking at the graph, we say that this distribution is skewed because one side of the graph does not mirror the other side. hey, you know generally between the ages zero and Hide Axis, Borders and White Spaces in Matplotlib, Visualization of Merge sort using Matplotlib, Visualization of Quick sort using Matplotlib, 3D Visualisation of Quick Sort using Matplotlib in Python, 3D Visualisation of Merge Sort using Matplotlib, 3D Visualisation of Insertion Sort using Matplotlib in Python. Press STAT 1:EDIT. How to change angle of 3D plot in Python? How to plot two histograms together in Matplotlib? matplotlib.pyplot.hist() function itself provides many attributes with the help of which we can modify a histogram.The hist() function provide a patches object which gives access to the properties of the created objects, using this we can modify the plot according to our will. Then the starting point is 0.5 and the ending value is 6.5. - Difficult to determine the distribution of data just by looking at the numbers. A histogram is a type of chart that allows us to visualize the distribution of values in a dataset. The following data are the shoe sizes of 50 male students. Once you have the Analysis Toolpak enabled, you can use it to create a histogram in Excel. We have one person. The following data are the number of sports played by 50 student athletes. The five numbers used to create a box-and-whisker plot are: The following graph shows the box-and-whisker plot. The following data are the number of books bought by 50 part-time college students at ABC College. How to Set a Single Main Title for All the Subplots in Matplotlib? And so you see that plotted A Select an answer of $, Help me please! Alright, what about 30 to 39? The middle [latex]50[/latex]% (middle half) of the data has a range of [latex]5.5[/latex] inches. a way of visualizing things. The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value. A value is counted in a class interval if it falls on the left boundary, but not if it falls on the right boundary. Where does the version of Hamapil that is different from the Gemara come from? In the Charts group, click on the 'Insert Static Chart' option. 20 to 29, which is gonna be this one, just getting, I'm writing too big. - Positively skewed The interval [latex]5965[/latex] has more than [latex]25[/latex]% of the data so it has more data in it than the interval [latex]66[/latex] through [latex]70[/latex] which has [latex]25[/latex]% of the data. Its a column chart that shows the frequency of the occurrence of a variable in the specified range. These are called bins. , h and the variable cost to produce each gallon of How to set border for wedges in Matplotlib pie chart? - Negatively skewed. And so these are the ages of everyone in the restaurant at that moment. I don't get it. At least [latex]25[/latex]% of the values are equal to five. With the above dataset, the bins would be the marks intervals. To construct a histogram, first decide how many bars or intervals, also called classes, represent the data. Once created, you can not use Control + Z to revert it. Here are the steps to make sure you get the correct result: With the result that you get, you can now create a histogram (which is nothing but a simple column chart). So you go around the restaurant and you write down everyone's age. The bars make it easy to see how the data points, or how the density of the data within each bin changes relative to the numeric variable. 0-10, 10- 20, 20-30, 30-40, 40-50 and their respective frequencies are 20,30,70,50,and 30 You can set the bucket size however you like, but you'll get much better clarity with equal sized buckets. The following data are the heights of [latex]40[/latex] students in a statistics class. Direct link to cammy b (camryn)'s post sadly me, Posted 5 years ago. Direct link to Abe's post So a histogram is showing, Posted 5 years ago. That wouldn't give us much information. have written histogram. Connect and share knowledge within a single location that is structured and easy to search. How do I manually specify bins in Matplotlib? That's this category. This is achieved by overlaying the frequency polygons drawn for different data sets. But I've already, that Also, it works with any plotting function and doesn't depend on np.bincount() or ax.bar(). Zero to nine. The heights that are 63.5 are in the interval 61.9563.95. The box plot gives a good, quick picture of the data. Also, if performance matters, because you want counts of unique integers, there are a couple of slightly more efficient methods (np.bincount) that I'll show at the end. 60 0.05 = 59.95 which is more precise than, say, 61.5 by one decimal place. In case youre using Excel 2013 or prior versions, check out the next two sections (on creating histograms using Data Analysis Toopack or Frequency formula). Why are players required to record the moves in World Championship Classical games? ages at the restaurant are. The largest value is 74, so 74 + 0.05 = 74.05 is the ending value. Create a box plot for each set of data. So, I like, sometimes it's called a bin. For instance, you might have a data set in which the median and the third quartile are the same. Maybe it's very family-friendly. Approximatelythe middle [latex]50[/latex] percent of the data fall inside the box. There are 3 feet in a yard. young adults with kids, or maybe grandparents up here, and they just bring a lot "Signpost" puzzle from Tatham's collection. I'd like to show a histogram of each of those values. A rule of thumb is to use a histogram when the data set consists of 100 values or more. There are different ways you can create a histogram in Excel: Lets see how to make a Histogram in Excel. Recognize, describe, and calculate the measures of location of data: quartiles and percentiles. Click the File tab and then select Options. There are two big advantages to this approach. Follow the steps you used to graph a box-and-whisker plot for the data values shown. Please suggest 5; 5; 5; 5; 5 This data can be represented using ranges of temperature and the number o elements or substances in these ranges. This means that there is more variability in the middle [latex]50[/latex]% of the first data set. All you need to do is visually assess whether the data points follow the straight line. Its a nice post. A simple example of a histogram is the distribution of marks scored in a subject. And then we have the 10 to 19. Press TRACE, and use the arrow keys to examine the box plot. The default chart is not always in the best format. Kawser And obviously this doesn't apply just to ages of people in a restaurant, it applies to all sorts Or sometimes someone might say how many in each of those bins? If the null hypothesis is never really true, is there a point to using a statistical test without a priori power analysis? The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample. And then all the different age groups. Histogram. Available online at www.gro-scotland.gov.uk/statime-series.html (accessed April 3, 2013). The height 74 is in the interval 73.9575.95. Two students buy six books. 3; 3; 3; 3; 3; 3; 3; 3. But frankly speaking, if you want to see all the descriptive statistics summary at one go, you should use Excels Analysis ToolPak. In most cases, analysts finish their journey just creating a histogram, but without knowing its four pattern, it is not possible to get hidden gem from the data that makes the histogram. distributed in this restaurant. They also show how far the extreme values are from most of the data. The following data set shows the heights in inches for the girls in a class of [latex]40[/latex] students. c) Process running low. He also rips off an arm to use as a sword. 64; 64; 64; 64; 64; 64; 64; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5; 64.5, 66; 66; 66; 66; 66; 66; 66; 66; 66; 66; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 66.5; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5; 67.5, 68; 68; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69; 69.5; 69.5; 69.5; 69.5; 69.5, 70; 70; 70; 70; 70; 70; 70.5; 70.5; 70.5; 71; 71; 71. Find the interval? Mound-shaped Skewed Uniform Data values are evenly distributed around mean Histogram is not symmetric Each data value occurs with roughly the same frequency Uniform SkewedMound-shaped Histogram resembles a rectangle More data values to one side of the mean than the otherMean, mode, and median all occur in the center of the data range Which of the Remember that the purpose of making a histogram (or scatter plot or dot plot) is to tell a story, using the data to illustrate your point. You can also use an interval with a width equal to one. So 10 to 19, there are three people. How to Add Title to Subplots in Matplotlib? histogram. That's because the last bin behaves differently than the others, as noted in the documentation for numpy.histogram: Therefore, what you actually should do is specify exactly what bin edges you want, and either include one beyond your last data point or shift the bin edges to the 0.5 intervals. The x-axis displays the values in the dataset and the y-axis shows the frequency of each value. Why did US v. Assange skip the court of appeal? Numbers of driving accidents for students in a large university in the U.S. So the next one is ages 10 to 19, then 20 to 29, then 30 to 39, and 40 to 49, 50 to 59, let me make sure you It's the, oops. Since each date is paired with the temperature reading for the day, we dont have to think of the data as being random. but let's actually make a visualization of this. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both. 69 we have one person. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. Here are the steps to create a Histogram chart in Excel 2016: The above steps would insert a histogram chart based on your data set (as shown below). It would automatically create six equally spaced bins and used this data to create the histogram. This add-in enables you to quickly create the histogram by taking the data and data range (bins) as inputs. How to Draw Rectangle on Image in Matplotlib? Thank you, Hello MF, To explain what's going on, let's skip matplotlib.pyplot.hist and just use the underlying numpy.histogram function. Three people. Posted 8 years ago. Notice that we get the counts we'd expect, but because we asked for 4 bins between the min and max of the data, the bin edges aren't on integer values. How to fill color by groups in histogram using Matplotlib? How to Set Tick Labels Font Size in Matplotlib? Its due tomorrow! The number of sports is discrete data since sports are counted. Again, this interval contains no data and is only used so that the graph will touch the x-axis. Plot a Point or a Line on an Image with Matplotlib. Rounding to the next number is often necessary even if it goes against the standard rules of rounding. We have one person. The [latex]IQR[/latex] for the first data set is greater than the [latex]IQR[/latex] for the second set. This company one-year-olds are there? lot fewer senior citizens. [latex]61[/latex]; [latex]61[/latex]; [latex]62[/latex]; [latex]62[/latex]; [latex]63[/latex]; [latex]63[/latex]; [latex]63[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]66[/latex]; [latex]66[/latex]; [latex]66[/latex]; [latex]67[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]69[/latex]; [latex]69[/latex]; [latex]69[/latex]. And then 50 to 59. Well one way to think about it, is to put these ages By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Do the bucket intervals need to have the same value? The heights are continuous data, since height is measured. If you're dealing with unique integer counts starting with 0, you're better off using numpy.bincount than using numpy.hist. Press F2 to get into the edit mode for cell E2. The first bin includes all the values below it. Can corresponding author withdraw a paper after it has accepted without permission/acceptance of first author. So this the number, number of folks. In this case, these are E2:E8. But as a histogram, we're Here's a sample of the code I use to generate the histogram: from matplotlib import pyplot as py py.hist(histogram_data, 49, alpha=0.75) py.title(column_name) py.xticks(range(49)) py.show() What does it mean to "count by weighing"? This is going to be the interval. A histogram shows bars representing numerical values by range of value. the first quartile and the median? What if we wanted center-aligned bins to better reflect the fact that these are unique values? Press STAT and arrow to CALC. Also, when the starting point and other boundaries are carried to one additional decimal place, no data value will fall on a boundary. The heights 60 through 61.5 inches are in the interval 59.9561.95. Working with Images in Python using Matplotlib, Python | Working with PNG Images using Matplotlib. Are there any canonical examples of the Prime Directive being broken that aren't shown on screen? Use one number line for both box plots. Everybody was like, To create a histogram in Excel, you provide two types of data the data that you want to analyze, and the bin numbers that represent the intervals by which you want to measure the frequency. The point labeled 44 represents the next interval, or the first real interval from the table, and contains four scores. Frequency distribution tables have important roles in the lives of data analysts. You may encounter box-and-whisker plots that have dots marking outlier values. Press WINDOW. How to upgrade all Python packages with pip, How to change the font size on a matplotlib plot, When to use cla(), clf() or close() for clearing a plot, Save plot to image file instead of displaying it, How to make IPython notebook matplotlib plot inline, Histogram height with Matplotlib and Python, User without create permission can create a custom object from Managed package using Custom Rest API. Presidents. Fact Monster. Histogram example: student's ages, with a bar showing the number of students in each year. The horizontal axis is used to plot the date or time increments, and the vertical axis is used to plot the values of the variable that we are measuring. Representing an experiment with two dices using matplotlib - wrong representation, Matplotlib - Histogram - First bin doesn't start at the beginning of X-axis. Otherwise the box plot may not be useful. The whiskers extend from the ends of the box to the smallest and largest data values. Histogram: Why use one? - Bi-modal We start with a standard Cartesian coordinate system. Two people. So let's do buckets or categories. Accessibility StatementFor more information contact us atinfo@libretexts.org. And then we have 40 to 49. Direct link to davenport52801's post So, if I did a histogram,, Posted 5 years ago. Plotting Various Sounds on Graphs using Python and Matplotlib, COVID-19 Data Visualization using matplotlib in Python, Analyzing selling price of used cars using Python, optional parameter contains integer or sequence or strings, optional parameter contains boolean values, optional parameter represents upper and lower range of bins, optional parameter used to create type of histogram [bar, barstacked, step, stepfilled], default is bar, optional parameter controls the plotting of histogram [left, right, mid], optional parameter contains array of weights having same dimensions as x, optional parameter which is relative width of the bars with respect to bin width, optional parameter used to set color or sequence of color specs, optional parameter string or sequence of string to match with multiple datasets, optional parameter used to set histogram axis on log scale. train has already left. However, if youre using Excel 2016, I recommend you use the inbuilt histogram chart (as covered below). How to Turn Off the Axes for Subplots in Matplotlib? By using our site, you And so when you just look at these numbers it really doesn't give How To Adjust Position of Axis Labels in Matplotlib? Now since you have the location of the edge of bins starting from left to right, display it as the xticks. The result is an array and you can not deletea part of the array. You May Also Like the Following Excel Tutorials: WTF??? Histograms are one of the most intuitive ways of representing the shape of a data set's distribution along a single numeric variable. Suppose you choose eight bars. And then finally, finally, ages 60-69. Alright, what about 40 to 49? Which box plot has the widest spread for the middle [latex]50[/latex]% of the data (the data between the first and third quartiles)? the distance between numbers on a graph of data display. 39 bin or bucket or category. Zero to nine, there are six people. I wrote histograph, I should How to center bin ticks in matplotlib histogram? What do hollow blue circles with a dot mean on the World Map? 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3 A graph that recognizes this ordering and displays the changing temperature as the month progresses is called a time series graph. Im really struggling on how to do this. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. You can specify conditions of storing and accessing cookies in your browser. only one peak? It's very straightforward! So how many people Why don't we just define if it says to, Posted 5 months ago. It is important to start a box plot with ascaled number line. Once the box plot is graphed, you can display and compare distributions of data. And on this axis I'm Alright. The horizontal axis is labeled with what the data represents (for instance, distance from your home to school). \(\dfrac{6.5 - 0.5}{\text{number of bars}}\) = 1. where 1 is the width of a bar. However, once the same data points are displayed graphically, some features jump out. So, if I did a histogram, I could record ages of people in my school and in the primary? This video explains what descriptive statistics are needed to create a box and whisker plot. The following data represent the number of employees at various restaurants in New York City. [latex]136[/latex]; [latex]140[/latex]; [latex]178[/latex]; [latex]190[/latex]; [latex]205[/latex]; [latex]215[/latex]; [latex]217[/latex]; [latex]218[/latex]; [latex]232[/latex]; [latex]234[/latex]; [latex]240[/latex]; [latex]255[/latex]; [latex]270[/latex]; [latex]275[/latex]; [latex]290[/latex]; [latex]301[/latex]; [latex]303[/latex]; [latex]315[/latex]; [latex]317[/latex]; [latex]318[/latex]; [latex]326[/latex]; [latex]333[/latex]; [latex]343[/latex]; [latex]349[/latex]; [latex]360[/latex]; [latex]369[/latex]; [latex]377[/latex]; [latex]388[/latex]; [latex]391[/latex]; [latex]392[/latex]; [latex]398[/latex]; [latex]400[/latex]; [latex]402[/latex]; [latex]405[/latex]; [latex]408[/latex]; [latex]422[/latex]; [latex]429[/latex]; [latex]450[/latex]; [latex]475[/latex]; [latex]512[/latex]. We can instead use the times given to impose a chronological order on the data.
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