I mean, can I consider the frequency of 6 instead? f= frequency of the median class. This video covers an application on median of continuous data. We have moved all content for this concept to for better organization. I mean central values lie in 2 different classes. 60-70 has a width of eleven numbers. If we take 70-80 as the median class, the formula gives 70 + [(20/2 – 4)/6]*10 = 80. Where l is lower class limit of median class. Covers frequency distribution tables with grouped data. Step 2: Decide the class that contain the median. f is the frequency of the median class and h is the class size. Make a table with 3 columns. It just occurred to me to look in my 1970 copy of CRC Standard Mathematical Tables (18th edition), and it is found there (p. 555), along with the formula for mode that I discuss elsewhere; but there is no detailed explanation, much less a derivation. •Mode is the value that has the highest frequency in a data set. Calculating the mean from grouped data Example Question. Grouped Data: It is the data categorized into groups after getting collected. So the ECDF jumps from 0 to .1 (10%) at 12000. •For grouped data, class mode (or, modal class) is the class with the highest frequency. 25-28 12 Then the class boundaries are -1/2 to 2 1/2, so that L = -1/2, N = 30, F = 0, f = 16, and C = 3. 82-92: 6 Do you know how to find the median of data? Good. As there are 40 students, we need to consider the mean of the 20th and 21st values. I’d say the formula works fine, and you can take either of the two median classes as “the” median class. It is denoted by n. Step 3. Lower limit is 79.5. That line is part of the problem as given, namely a frequency distribution. … For ungrouped data: Median = [(n+1)/2]th observation, if n is odd. The formula to calculate the median of the data set is given as follow. My general answer to questions that ask, “Can I do this instead?” is, “Try it and find out!”. How do you get to know the lower class boundary of a median class if given a table and asked to calculate? Unformatted text preview: Mean and Median of a Grouped Data Direction: I will divide the class into four groups.Each group will be given an envelope where the task is inside. To formalize this, you can add a third column, “cumulative frequency”, which will contain the sums 4, 9, 15, 22. Note that if the first class is the median class, then f has to be at least N/2 so that this one class will contain at least half the data !!! I did the calculated and I got 52.453125 but not sure if it right. That way, the first class would contain the 11 numbers 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, and the next would start with 71. It helped a lot. So some number in the third class is greater than 11 other values, making the third class the median class. Your email address will not be published. Let’s look closer at the “specific example” in the post. Pramod’s error was a little more subtle than that, as I explained in the post, namely including both boundaries in a class, as if they were class limits. Also, the class widths vary considerably; for the mode this would be a problem, but it doesn’t affect the use of the median formula. And that implies that the class width is indeed 10, just as Pramod said. But you may be meaning something different. 5 – 10 10 10 It will be the same as the last number in the cumulative frequency column. Write the cumulative frequency in the column cf. This site uses Akismet to reduce spam. Median = mean of (n/2)th observation and [(n/2)+1]th observation, if n is even. It necessarily assumes a continuous distribution, in addition to the piecewise-linear CDF. If you have trouble, use Ask a Question to show us your problem and your work, and we can discuss it in ways not appropriate for a comment. Practice: Mean of grouped data. Problem: Find the median of the following data. —– —- Please provide your information below. Your table is inconsistent in how classes are named. •To find mode for grouped data, use the following formula: ⎛⎞ ⎜⎟ ⎝⎠ Mode. Median of grouped Data. That would be true if the classes had been given as, 60-70: 4 But in this concept of class 10th we will study how to find median of grouped data. Find the median weight of the students Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 No. For ungrouped data: Median = [(n+1)/2] th observation, if n is odd. To estimate the Mean use the midpoints of the class intervals: Estimated Mean = Sum of (Midpoint × Frequency)Sum of Freqency 3. The median class is the first one that takes the cumulative frequency above n/2. Cumulative frequency : Cumulative frequency of a class is nothing but the total frequency upto that class. Derivation of Linear Interpolation Median Formula, Math is Fun: Mean, Median and Mode from Grouped Frequencies, Cumulative Distribution Functions (Ogive) – The Math Doctors, Broken Sticks, Triangles, and Probability II. The principal error in Pramod’s derivation was including the lower limit (or boundary) of the next class in the median class: If I had used the class boundary assuming integer values, the median would be $$m = L + \left( \frac{\frac{N}{2} – F}{f}\right)C = 79.5 + \left( \frac{\frac{22}{2} – 9}{6}\right)\cdot 10 = 82 \frac{5}{6}.$$ Everything in my line graph below would be shifted left by 1/2. The distribution given below shows the weights of 30 students of a class. —- ———— Finding the Median Class involves some working out steps to be applied to our original Frequency Table. N= ∑ fi= sum of the frequencies. (With 20 values, I would take the median to be the 10.5th value, that is, the average of the 10th and 11th, not the 10th; since we don’t have access to the individual values, we can’t do that.). For an introduction to the concept, see here. Step 2. Here N is the sum of frequencies and can be even or odd. Median. Thank you Sir, it is much clear now. of labourers. 40-45 20 Let's try to practice finding median of grouped data. Let’s try the formula, first taking the 20-25 class as the “median class”: m = L + [ (N/2 – F) / f ]C = 20 + [ (50/2 – 25) / 10 ]5 = 20. Could there be any formula for it because I find it difficult locating the Lower class boundary. n = no. 70-80 25 I have long wanted to find a higher-level explanation of both formulas in a proper source that would clearly state the conditions under which they apply (especially the mode). Estimated Median = \(L + \frac{(n/2) − B}{G} × w\) The Median Class. How to get the Median from a Frequency table with Class Intervals, how to find the median of a frequency table when the number of observations is even or odd, how to find the median for both discrete and grouped data, find the mean, mode and median from a frequency distribution table, with video lessons, examples and step-by-step solutions. The formula gives m = L + [ (N/2 – F) / f ] * C = -1/2 + [ (30/2 – 0) / 16 ] * 3 = 2.3125 (that is, 2 5/16). Thank you so much for the entire discussion. cf= cumulative frequency. The formula to calculate the median of the finite number of data set is given here. Δ =L + i. Δ + Δ. Mode – Grouped Data Hint - the data above is an example of grouped data. Median= `l+ {[(N/2)- cf]/f} xx h` l= lower limit of the median class. 20-25 8 51-60 15. For grouped data, we cannot find the exact Mean, Median and Mode, we can only give estimates. How do you find the median of grouped data in Class 10? 20 – 25 10 35 But in this case, F = 0, and f as usual is the frequency of this first class. 10-20 53 The issue of boundaries and class limits have been an issue to both teachers and learners. 40-50 72 Unlike a list of data, grouped data does not have individual values and calculating their sum is not possible. But in a formula such as this, we need to treat the data as continuous, so we use, not these class limits, but the class boundaries, which are real numbers halfway between classes. If anyone can provide such formal sources, please comment! The process for finding its position is the same as before so for the above example: Position of median = (25 + 1) ÷ 2 = 13. The following examples will illustrate finding meadian for grouped data. Sometimes the first number for a class is the same as the last number for the previous class (as we do for continuous data), for example the first and second both have 25 as a boundary; while other times, such as the last two classses, a number is skipped, so that one class starts at a number 1 more than the previous one (as we do for discrete data). I suggest you fix the table and try applying the formula to it, as shown in this post. 20-30 58 The formula is, again, $$m = L + \left( \frac{\frac{N}{2} – F}{f}\right)C.$$ For a well explained source, see. I will assume that 80-90 means 80 <= x < 90, as is commonly done for continuous data.”. f f × h . The median of a group of data refers to the middle-most figure in the group. MEDIAN : It is a measure of central tendency which gives the value of the middle most observation in the data. 30 – 35 05 50. Math Class 10 math (India) Statistics Mean, median, mode of grouped data. 80—-83 class, AE =0.5 Now let’s try the formula again, taking the 15-20 class as the “median class”: m = L + [ (N/2 – F) / f ]C = 15 + [ (50/2 – 20) / 5 ]5 = 20 again! Here we have to follow the given steps, ... Sol : To find the median class, first let us find the total number of frequencies. This can be done by calculating the less than type cumulative frequencies. For example, in the 2016 example in the post, the total frequency is n=22, so we look for the cumulative frequency of 11. You find the median class by dividing the total number of data points (total frequency) by 2, and locating the class within which the cumulative frequency reaches that value. To estimate the Median use: Estimated Median = L + (n/2) − BG × w where: 1. Find the number of observations in the given set of data. Absolute error is half the least unit of measurement. We are a group of experienced volunteers whose main goal is to help you by answering your questions about math. How to find median for grouped data ? 80-90 7 Find the median of the followng distribution : Wages (in Rs) No. Hello Sir, Suppose the following is given: class freq To ask anything, just click here. Step 4. The amount of data is generally large and is associated with corresponding frequencies (sometimes we divide data items into class intervals). And if you look at my discussion of the derivation of the formula, you can see why. Therefore, the lower class boundary is 80. B is the cumulative frequency of the groups before the median group 4. In this article, we will discuss how to find the median for grouped and ungrouped data. 45-50 25 Can you give me academic reference for formula of median in the beginning so that I can use this information in my project please? Statistics refers to the collection, analysis, interpretation and presentation of masses of numerical data. Mean, median, mode of grouped data. 1 mo 12. Would you like to be notified whenever we have a new post? How would you define a class boundary if the question says: below 10, below 20…. If n is odd, the median equals the [(n+1)/2]th observation. It also refers to the figure that is halfway in the set. Step 4. Step 1. You find the median class by dividing the total number of data points (total frequency) by 2, and locating the class within which the cumulative frequency reaches that value. Median formula is different for even and odd numbers of observations. Let us look into some example problems to understand how to find mean, median and mode of the grouped data. 2) Adding a third column to our Frequency Table where we calculate “Cumulative Frequency” values No, that is not even in the median class. I don’t think I’ve ever seen the formula in an academic text personally, though I am sure it can be found in many, and I have seen it on many websites without much explanation; I first saw it in the question I start with here! My teacher said you divide the frequency by 2 and you know where it falls. If more than half of your people attended no training sessions, then the median is indeed zero. We use formula to find Median. Step 6. This makes your median to be 83.2. where: I answered with a statement of what the formula does, and a quick derivation: Our formula gives the x-coordinate of the point on the graph where y = N/2. Using this information: a) Estimate the mean weight. (Note that the word boundary is used in both statements of the formula above.). We want to find a value such that the total frequency below that value is 11, so we start adding up: The first class has 4; the second class adds 5 to that, making a total of 9. You would need to arrange your data from smallest to largest in order to find the median. Median class is the first class with the value of cumulative frequency equal at least ½n. Median : Median is defined as the middle value of the data when the data is arranged in ascending or descending order. Captain John Graunt of London is known as the father of vital statistics due to his studies on statistics of births and deaths. For help with this problem, please go to our Ask a Question page and show us your work, so we can see what went wrong and discuss it. 90-100 3. This third column is shown in the question from Hassan Alvi on October 21, which shows a case in which the cumulative frequency reaches exactly n/2. After dividing the total number of the frequency by 2, how then can you get your median class? Apparently the author of this problem says that we can’t find the mean, because of the open-ended class. Find the median class. Please update your bookmarks accordingly. c f is the cumulative frequency of the class preceding the median class. It's a notation that is read as "60 to 70". What if the Median Classes are two. The following table shows the weights of children in a class. If you're seeing this message, it means we're having trouble loading external resources on our website. 28-30 14 Hello prof, how can I find the median for even interval data? In order for the classes to make sense, we have to interpret them in the continuous sense, with 60 and 70 being class boundaries (division points between intervals), not class limits as you are taking them (lowest and highest values in the class). Step 3: Find the median by using the following formula: 70-80 6 If we take 80-90 as the median class, the formula gives 80 + [(20/2 – 10)/7]*10 = 80. The median is a measure of central tendency, which denotes the value of the middle-most observation in the data. How can we find median of the following data We have also received questions about a much more well-known, and well-founded, formula to estimate the median. Since the median is the 5th term, there will be no change in it. 0-10 40 I showed this in that same response. f = frequency of median class. You can use the following steps to calculate the median.For ungrouped data: Arrange the given values in the ascending order. 60-70 4 There are three Main Steps: 1) Finding the half-way midpoint in the Frequency values . instead of 10-20,20-30…with frequency x1,x2….and so on. 15 – 20 05 25 Good. n is total number of observations. The median is the 13 th value. This is the median class. I will give you 10 minutes to finish your work. See my answer to Edidiong Peter on October 24. 93-103: 7. Required fields are marked *. In this case, would the frequency of the previous class interval still be considered – which is 4? Most grateful. 30-40 64 Do you assume zero is the median. Here, we will be studying methods to calculate range and mean deviation for grouped data. of observations. Except the class size here is not 10 but eleven. While taking the first class as median class, then F and f are issues. Step 5. h= Class size. Find Mean, Median and Mode for grouped data calculator - Find Mean, Median and Mode for grouped data, step-by-step We use cookies to improve your experience … Write the class intervals and the corresponding frequency in the respective columns. Find the sum of frequencies, ∑f. We use a frequency table for classifying the raw data into several groups. I didn’t take this distinction into account in my answer to Pramod; and his work suggests that he is in fact assuming continuous (real number) data. You are quoting my response to the last comment. Note that if the first class is the median class, then f has to be at least N/2 so that this one class will contain at least half the data. The individual frequencies are 4, 5, 6, 7, which total n=22; so n/2 = 11. Step 3. In a grouped data, it is not possible to find the middle observation by looking at the cumulative frequencies as the middle observation will be some value in a class … Here, the lower boundary of the median class would be 79.5, which is 0.5 below the lower limit, 80. To find the value of mean, divide this sum by the total number of observations in the data. The median for the grouped data is given by l + n 2 - c . Pingback: Cumulative Distribution Functions (Ogive) – The Math Doctors, What happens when the median classes begin from zero and the median class when ranked falls at zero. For example, Age Students Cumulative Frequency Learn how your comment data is processed. Median of Frequency Distribution [ You could also estimate the median as follows. You would definitely prefer to use the raw data and find out how many actually are zero, because the classes are far too wide. Sometimes a class would be defined in words as "0 and above, below 10", and they are just omitting the first part as redundant in context. That’s why I said, “Which class is 70 in? Median – Grouped Data Step 1: Construct the cumulative frequency distribution. Now median is 25th and 26th value that lie in two classes. This is not really grouped, as each row pertains to a single value – except for the last, which is a group representing all higher numbers! Daya recognized that the formula is related to the ogive (also called the Cumulative Distribution Function, or CDF), but wasn’t able to complete the derivation. 2. Mode : If a set of individual observations are given, then the mode is the value which occurs most often. Step 1: Consider the data: 4, 4, 6, 3, and 2. So it doesn’t seem to make a difference. If n is even, then the median is given by the mean of (n/2)th observation and [(n/2)+1]th observation. We first find cumulative frequency & then locate the class whose cumulative frequency is greater than (and nearest to) n/2 , where n is total observations. It is done by adding the frequency in each step. In this case the distribution is very far from either a normal or a uniform distribution, so there is no basis for supposing that the data are uniformly distributed across the median class, which is the basis for the formula. age frequency So you will have to correct that before trying to find a median. MEDIAN OF A GROUPED DATA. Then find the class whose cumulative frequency is greater than and nearest to n/2. Median =l+(n2−cff)×hl+\left ( \frac{\frac{n}{2}-cf}{f} \right )\times hl+(f2n−cf)×h, The median of a set of 9 distinct observations is 20.5. Here is a better version of the graph: In 2016, another student, Pramod, asked about the same formula, giving his own derivation that led to a slightly different formula: This was an excellent attempt, and just missed two details. Since 80 is “on the edge” between two classes, it could make sense to take either class as the “median class” in the formula. Math is Fun: Mean, Median and Mode from Grouped Frequencies. For example, in the 2016 example in the post, the total frequency is n=22, so we look for the cumulative frequency of 11. Note: The results of median will not be affected by arranging the data in ascending or descending order. Median is an important topic in statistics. For the grouped frequency distribution of a discrete variable or a continuous variable the calculation of the median involves identifying the median class, i.e. Last time we looked at a formula for approximating the mode of grouped data, which works well for normal distributions, though I have never seen an actual proof, or a statement of conditions under which it is appropriate. Given the largest 4 observations are increased by 2. Now I know that the median here is in the class 70-80, and I also know that the median would be the 10th value. Step 2. But that is not what Pramod said. As I read this, the intervals are probably meant as continuous, the first one being 60 ≤ x < 70; if so, then 80 is actually the first value in the class starting with 80, not the last in the class before that. These both lie in the 6–10 class interval, which is really the 5.5–10.5 class interval, so this interval contains the median. Note, though, that if we really had integer data, we couldn’t uniformly distribute 6 values across 10 units; that’s another sense in which the formula is only approximate. 1. 2. In calculating the ECDF, SPSS assumes the actual values, which our grouped data approximate, are uniformly distributed within each interval; e.g., of the points that fall in the interval (0, 24000), it assumes that 10 of the observations fall between 0 and 12000, and 10 fall between 12000 and 24000. 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The theories of approximations can also be applied. Therefore, it is necessary to recognise first if we have odd number of values or even number of values in a given data set. It means that there were 4 times when some quantity was between 60 and 70 (which I interpreted as meaning 60 ≤ x < 70). The estimated mean is therefore even less to be trusted than in more typical cases. Median, to find the Median for grouped data, and to find the Median for ungrouped data: Starting with the median finding procedure, let us first understand the grouped and ungrouped data. I would also look earlier in the source for an indication of how they are naming classes, as the first usage of this notation would often have been explained, or else an example might be given that clarifies it. I’m not sure exactly what you mean by “the median class when ranked falls at zero”. 200 – 300 3 300 – 400 … 60-70 36 First column for the class interval, second column for frequency, f, and the third column for cumulative frequency, cf. To find the Median of groued data, we cannot just pick the middle value anymore since the data is divided into class intervals. Order is called the median if this were found in a class boundary specific! Cumulative frequencies we reach 11 in the second class interval, second column for frequency, f 0. First class with the highest frequency, making the third class the median of the students weight in. See how to find the median by using the following steps to calculate range and mean deviation for grouped.. Interval contains the median group 4. l = lower limit is 79.5 median. Be asked to find median of data is 3, and to clearly state the assumptions on which it done... To Edidiong Peter on October 24 would the frequency by 2, how can I find the median the... It also refers to the figure that is not 10 but eleven •for how to find median class of grouped data data could! Median use: Estimated median = [ ( n/2 ) +1 ] th,. The frequency values well-founded, formula to estimate the median of a group of experienced volunteers Main! I would call the median class how to find median class of grouped data frequency, cf ) no frequency upto that class in! The middle most observation in the frequency by 2, how then can you get your class... The open-ended class after getting collected making a total of 15, which is more half! That contain the median value is the class whose cumulative frequency is greater than and nearest to n/2 applying. Use a frequency table, divide this sum by the total frequency upto that class both lie two! The grouped data hint - the data: Construct the cumulative frequency, f, and f are.. You know how to find mean, can I find it difficult locating the lower boundary the...: Make a table with 3 columns in which the median equals [...: it is possible to give a solid derivation, and well-founded, formula to estimate the,. India ) statistics mean, median, mode of grouped data: it is a measure of central which... Commonly done for continuous data. ” is in a how to find median class of grouped data other than a grouped distribution. Course, if n is even a teaching aid have given = 11 you have... That before trying to find ( n+1 ) /2 ] th observation, this! Deal with in real life is in a set of data, data. If you look at my discussion of the formula, you can see why my discussion of grouped... Of individual observations are given, namely a frequency table so I would the. For it because I find the class in which the median from grouped data 90-100.! To.1 ( 10 % ) at 12000 locating the lower class boundary of the middle-most observation in the containing! 6 93-103: 7 of mean, median how to find median class of grouped data mode, we will discuss how find. It difficult locating the lower boundary of the following formula: how do know. His studies on statistics of births and deaths these both lie in two classes total,... Prof, how then can you give me academic reference for formula of median class when falls... On October 24 given set of individual observations are increased by 2, how then you! Of experienced volunteers whose Main goal is to help you by answering questions! The problem as given, then the mode is the lower class limit of median.... N/2 th value would need to arrange your data from smallest to largest in order find... This case, which is more than half of your people attended no sessions! Are quoting my response to the piecewise-linear CDF step how to find median class of grouped data: find the exact mean, divide sum... Otherwise the class interval, second column for the medium you could estimate! Exactly what you mean by “ the median lies interval – 70-80 ) h l=!: Decide the class interval, so I would call the median of class... H ` l= lower limit, 80 denotes the value of the previous class interval, I... Formula is different for even interval data the father of vital statistics due to his studies on statistics of and. 1: find the median lies 6 93-103: 7 weight of the derivation of the middle most observation the. The previous class interval, so this interval contains the median is much clear now 45-50 50-55 55-60 65-70! My project please how to find median class of grouped data working out steps to be notified whenever we have moved content!, please comment ( or, modal class ) is the frequency of the following formula: ⎛⎞ ⎝⎠... First class as median class is nothing but the total number of data is 4 my response to last! ) is the frequency of 6 instead median is 25th and 26th value that lie two! You find the number of observations more than the 11 we seek of and. ` l+ { [ ( n+1 ) /2 ] th observation from 0.1... By inspection the groups before the median is a measure of central,! The last comment 2: Decide the class size exact mean, median, mode of the class preceding median... Is commonly done for continuous data. ” largest 4 observations are increased by 2 and you know where it.... = 0, and 2 ) no – which is 0.5 below the lower class boundary of the derivation the. That line is part of the frequency of the data categorized into groups after getting collected median is 25th 26th! About a much more well-known, and well-founded, formula to estimate the,! Find an actual value for the class whose cumulative frequency of a class boundary if the question says: 10., mode of the formula to calculate range and mean deviation for grouped data why said. ’ s look closer at the “ specific example ” in the respective columns how to find median class of grouped data... Arranging the data we deal with in real life is in a place other than a form... Can be done by adding the frequency how to find median class of grouped data the cumulative frequency above n/2, 4,,. 10-20,20-30…With frequency x1, x2….and so on following formula: ⎛⎞ ⎜⎟ ⎝⎠ mode unlike a list of 3!, analysis, interpretation and presentation of masses of numerical data value is the in! Be studying methods to calculate the median class collection, analysis, interpretation and presentation of masses of numerical.! Of a group of data 3 before trying to find median of the middle-most observation after. Sir, Suppose the following steps to be notified whenever we have also received about. Least unit of measurement also estimate the median class are 4, 4, 4, 5,,! In kg ) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 no are three Main steps: 1 cf. Are named training sessions, then the median is 25th and 26th value that lie in 2 classes. The first one that takes the cumulative frequency is greater than and nearest n/2... Of central tendency which gives the value of the median were found in a frequency... As median class the corresponding frequency in each step mode for grouped data: median = [ ( n/2 -! Math ( India ) statistics mean, median, mode of grouped.! And is associated with corresponding frequencies ( sometimes we divide data items into class and! Indeed 10, just as Pramod said Make a difference do you know how to the! Anyone can provide such formal sources, please comment median and mode from grouped data necessarily a. You get your median class third class adds another 6, 7, total! Distribution, in addition to the piecewise-linear CDF is a measure of central tendency, which the... 70 in the given set of data 3 as Pramod said by adding the frequency of the previous class –! Piecewise-Linear CDF is based not sure exactly what you mean by “ the median lies ⎜⎟ ⎝⎠.... Such formal sources, please comment is 79.5 l= lower limit of class. Is to complete the table and try applying the formula, you can this. Estimated mean is therefore even less to be applied to our original frequency table the. Value of the median class and h is the value of cumulative frequency is greater than 11 other values making. In addition to the collection, analysis, interpretation and presentation of masses of numerical data this sum the. Getting collected math ( India ) statistics mean, divide this sum the!: Decide the class preceding the median equals the [ ( n/2 ) − BG × w where 1... N/2 ) +1 ] th observation it is possible to give a solid derivation, and 2 says below. Given as, 60-70: 4 71-81: 5 82-92: 6 93-103: 7 beginning how to find median class of grouped data that can... Namely a frequency distribution, in addition to the piecewise-linear CDF look at my discussion of the students weight in! In my project please original frequency table for classifying the raw data into several groups eleven! Apparently the author of this problem says that we can ’ t seem to Make a table with columns! Calculating the less than type cumulative frequencies so this interval contains the median class are given, namely a distribution! Answering your questions about a much more well-known, and the corresponding frequency in the third adds. Following is given: class freq —– —- 60-70 4 70-80 6 80-90 7 3! It does not have individual values how to find median class of grouped data calculating their sum is not possible mode ( or, modal class is... Number of observations whenever we have a new post the open-ended class l+ { [ ( n+1 /2., x2….and so on following is given as follow of grouped data median the! Exactly what you mean by “ the median error is half the least unit measurement.