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1. Top results related to finding the median of grouped data

   • Median of Grouped Data: Formula, How to Find, and Solved Examples

     Median of Grouped Data is the value of the middlemost data point in any dataset when dataset is grouped. For ungrouped data, it is easy to find the median but finding the Median of Grouped Data is slightly complex. When we have any data in statistics, we try to find some basic parameters related to it which provide ease in data interpretation and making further predictions related to data. To measure the central tendency of data, i.e., a single value that can be used to represent an entire distribution, we generally have three parameters: mean, median, and mode.

     In this article, we will discuss what is meant by Grouped Data and Median of Grouped Data. We will also learn about the Formula for Median of Grouped Data and steps to calculate the Median of Grouped Data, solved examples, and some frequently asked questions as well.

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     Table of Content

     How to...

     • What is Grouped Data?
     • What is Median of Grouped Data?
     • Median of Grouped Data Formula
     • How to Calculate Median of Grouped Data?

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   • Finding the median of medians of quicksort

     Top Answer

     Answered Jun 10, 2013 · 1 votes

     The median-of-medians algorithm doesn't work by finding the median of each block of size 5 and then running a sorting algorithm on them to find the median. Instead, you typically would sort each block, take the median of each, then recursively invoke the median-of-medians algorithm on these medians to get a good pivot. It's very uncommon to see the median-of-medians algorithm used in quicksort, since the constant factor in the O(n) runtime of the median-of-medians algorithm is so large that it tends to noticeably degrade performance.

     There are several possible improvements you can try over this original approach. The simplest way to get a good pivot is just to pick a random element - this leads to Θ(n log n) runtime with very high probability. If you're not comfortable using randomness, you can try using the introselect algorithm, which is a modification of the median-of-medians algorithm that tries to lower the constant factor by guessing an element that might be a good pivot and cutting off the recursion early if one is found. You could also try writing introsort, which uses quicksort and switches to a different algorithm (usually heapsort) if it appears that the algorithm is degenerating.

     Hope this helps!

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     2/5

   • Finding the median of an unsorted array

     Top Answer

     Answered Nov 08, 2014 · 52 votes

     You can use the Median of Medians algorithm to find median of an unsorted array in linear time.

     Other Answers

     Answered Nov 22, 2016 · 15 votes

     I have already upvoted the @dasblinkenlight answer since the Median of Medians algorithm in fact solves this problem in O(n) time. I only want to add that this problem could be solved in O(n) time by using heaps also. Building a heap could be done in O(n) time by using the bottom-up. Take a look to the following article for a detailed explanation Heap sort

     Supposing that your array has N elements, you have to build two heaps: A MaxHeap that contains the first N/2 elements (or (N/2)+1 if N is odd) and a MinHeap that contains the remaining elements. If N is odd then your median is the maximum element of MaxHeap (O(1) by getting the max). If N is even, then your median is (MaxHeap.max()+MinHeap.min())/2 this takes O(1) also. Thus, the real cost of the whole operation is the heaps building operation which is O(n).

     BTW this MaxHeap/MinHeap algorithm works also when you don't know the number of the array elements beforehand (if you have to resolve the same problem for a stream of integers for e.g). You can see more details about how to resolve this problem in the following article Median Of integer streams

     Other Answers

     Answered May 19, 2012 · 11 votes

     Quickselect works in O(n), this is also used in the partition step of Quicksort.

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     3/5

   • Finding the median of a range of values selected using vlookup

     Top Answer

     Answered Sep 02, 2016 · 0 votes

     Since your column A values are ordered ascendingly, we can use the very efficient:

     =MEDIAN(INDEX(B2:B18,MATCH(B21,A2:A18)):INDEX(B2:B18,MATCH(B22,A2:A18,0)))

     Regards

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     4/5

   • Finding the median of numbers in a LinkedList

     Top Answer

     Answered May 17, 2009 · 3 votes

     The best algorithm is QuickSelect

     Read the article and try to understand QuickSort - The concept is similar.

     Check all answers on Stack Overflow

     5/5

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2. Videos

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     Mean, Median, and Mode of Grouped Data & Frequency Distribution Tables Statistics

     Jan 26, 2019

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     How to calculate Median for Grouped Data? | Formula for Median of Grouped Data

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     Median for grouped data (Descending Order)

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3. www.statology.org · median-of-grouped-dataHow to Find the Median of Grouped Data (With Examples)

   www.statology.org · median-of-grouped-data

   

   Feb 11, 2022 · This tutorial explains how to calculate the median value of grouped data, including several examples.

4. People also ask

   How do you find the mean and median of a group?

   • For grouped data, we cannot find the exact Mean, Median and Mode, we can only give estimates. Estimated Mean = Sum of (Midpoint × Frequency) Sum of Frequency L is the lower class boundary of the group containing the median B is the cumulative frequency of the groups before the median group

   Mean, Median and Mode from Grouped Frequencies - Math is Fun

   www.mathsisfun.com/data/frequency-grouped-mean-median-mode.html

   See all results for this question

   How do you find the median height of a grouped data set?

   • Cumulative frequency of the class preceding the median class, cf = 11. We know that the formula to find the median of the grouped data is: Median = 149.03. Therefore, the median height for the given data is 149. 03 cm. The median of the following data set is 525. Find the values of x and y, if the total frequency is 100.

   Median of Grouped Data (Formula and Examples) - BYJU'S

   byjus.com/maths/median-of-grouped-data/

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   How do you find a median class?

   • Where L = Lower limit of the Median class. Median class is that class whose cumulative frequency is equal to or greater than the value of N/2 i = Size of the class interval. Compute the cumulative frequency of the distribution from lower end. Find out the median class.

   Measures of Central Tendency: Mean, Median and Mode | Statistics

   www.yourarticlelibrary.com/education/statistics/measures-of-central-tendency-mean-median-and-mode-statistics/91992

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5. byjus.com · maths · median-of-grouped-dataMedian of Grouped Data (Formula and Examples) | How to Find ...

   byjus.com · maths · median-of-grouped-data

   

   The formula to find the median of grouped data is: Median = l+ [((n/2) – cf)/f] × h Where l = lower limit of median class, n = number of observations, h = class size, f = frequency of median class, cf = cumulative frequency of class preceding the median class.

   • In statistics, the median is the middle value of the given dataset.
   • If the number of observations (n) is odd, the median is the (n+1)/2 th observation.
   • If the number of observations (n) is even, the median is the average of n/2th and (n/2)+1 th observation.
   • The median class is the class interval whose cumulative frequency is greater than (and nearest to) n/2.

6. www.geeksforgeeks.org · median-of-grouped-dataMedian of Grouped Data: Formula, How to Find, and Solved Examples

   www.geeksforgeeks.org · median-of-grouped-data

   

   Oct 10, 2023 · Median of Grouped Data is the value of the middlemost data point in any dataset when dataset is grouped. For ungrouped data, it is easy to find the median but finding the Median of Grouped Data is slightly complex.

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8. statisticalpoint.com · median-of-grouped-dataHow to Find the Median of Grouped Data (With Examples)

   statisticalpoint.com · median-of-grouped-data

   

   Jan 17, 2023 · While it’s not possible to calculate the exact median since we don’t know the raw data values, it is possible to estimate the median using the following formula: Median of Grouped Data = L + W [ (N/2 – C) / F] where: L: Lower limit of median class. W: Width of median class.

9. www.mathsisfun.com · data · frequency-grouped-meanMean, Median and Mode from Grouped Frequencies - Math is Fun

   www.mathsisfun.com · data · frequency-grouped-mean

   

   To estimate the Median use: Estimated Median = L + (n/2) − BG × w. where: L is the lower class boundary of the group containing the median; n is the total number of data; B is the cumulative frequency of the groups before the median group; G is the frequency of the median group; w is the group width; To estimate the Mode use:

10. www.cuemath.com · data · median-of-grouped-dataMedian of Grouped Data - Formula, Class 10, How to Find?

    www.cuemath.com · data · median-of-grouped-data

    

    Median of grouped data is the middle value of the data that is continuous and is written in the form of a frequency distribution table. The median formula of class 10 to find the median of grouped data in the form of frequency distribution is l + [ (n/2−c)/f] × h.

11. www.themathdoctors.org · finding-the-median-ofFinding the Median of Grouped Data – The Math Doctors

    www.themathdoctors.org · finding-the-median-of

    

    Dec 26, 2018 · This formula is used to find the median in a group data which is located in the median class. Median, m = L + [ (N/2 – F) / f ]C. L means lower boundary of the median class. N means sum of frequencies. F means cumulative frequency before the median class. Meaning that the class before the median class what.