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Quartile Formula - What is Quartile Formula?

The median of the set of the data values towards the left of this median forms the lower quartile and the median of the set of data points towards the right of this median forms the upper quartile.

Quartile

the three points that divide the data set into four equal groups in descriptive statistics

$q(0.25)$

In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to … Wikipedia

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Quartile - Wikipedia

October 30, 2025 - If there are (4n+1) data points, then the lower quartile is 25% of the nth data value plus 75% of the (n+1)th data value; the upper quartile is 75% of the (3n+1)th data point plus 25% of the (3n+2)th data point.

Computing methods

Computer software for quartiles

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Box Plots and Quartiles - GCSE Higher Maths - YouTube

November 17, 2023

Find the Lower Quartile and Upper Quartile - YouTube

Quartiles | Lower Quartile, Median, and Upper Quartile | Math with Mr.

How to Find the Lower Quartile Q1, upper Quartile Q3 and ...

October 14, 2023

How to Find Quartiles (Even Set of Data) | Math with Mr. J - YouTube

Quartiles from a List - Corbettmaths - YouTube

December 3, 2021

People also ask

How do I find the lower quartile?

The lower quartile can be found with two methods. The first method is to take the data, split it into two equal halves, and then find the middle of the lower half. Method 2 is to use the lower quartile formula in which you find the total number of data values, add 1, and then divide by 2. This number will represent what position the lower quartile will be within the list of the data values.

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Finding the Lower Quartile | Definition, Calculation & Examples ...

Is the minimum the lower quartile?

No, the minimum is not the lower quartile. The minimum is the smallest data value in the data set, while the lower quartile is the number that is in the middle of the lower half of the data set.

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Finding the Lower Quartile | Definition, Calculation & Examples ...

How do you find the upper and lower quartiles?

To find the up and lower quartile, first, find the median or middle quartile. Finding this number will separate the data into two equal halves. The lower quartile is the middle of the lower half and the upper quartile is the middle of the upper half.

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Finding the Lower Quartile | Definition, Calculation & Examples ...

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Finding the Lower Quartile | Definition, Calculation & Examples - Lesson | Study.com

June 29, 2019 - The first method is to take the data, split it into two equal halves, and then find the middle of the lower half. Method 2 is to use the lower quartile formula in which you find the total number of data values, add 1, and then divide by 2.

Statistics Canada

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4.5.1 Calculating the range and interquartile range

Then you need to split the lower half of the data in two again to find the lower quartile. The lower quartile will be the point of rank (5 + 1) ÷ 2 = 3. The result is Q1 = 15. The second half must also be split in two to find the value of the upper quartile.

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Quartiles & Quantiles | Calculation, Definition & Interpretation

June 21, 2023 - First quartile: Also known as Q1, or the lower quartile.

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Quartile Calculator | Interquartile Range Calculator

Find the median. This is the second quartile Q2. At Q2 split the ordered data set into two halves. The lower quartile Q1 is the median of the lower half of the data.

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Quartiles and interquartile range - Range and box-and-whisker plots - WJEC - GCSE Maths Numeracy (WJEC) Revision - BBC Bitesize

February 27, 2023 - So the lower quartile (LQ) is 4.

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Understanding Quartiles: Definitions, Calculations, and Examples

August 3, 2025 - Quartiles further break down the data set into quarters, which include a lower quartile (25% mark), median (50% mark), and upper quartile (75% mark). Calculating quartiles can be done manually using formulas or more efficiently in spreadsheets ...

Statistics By Jim

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Lower Quartile - Statistics By Jim

May 17, 2025 - It separates the lowest 25% of values from the highest 75%. In other words, one-quarter of the data fall at or below the lower quartile, while the remaining 75% lie above it.

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Quartile - GCSE Maths - Steps, Examples & Worksheet

August 11, 2023 - 5. Raheem writes down how long his bus journey to school takes on 20 different days. The times are given to the nearest minute. Find the lower and upper quartiles for his data set. ... Use the formulae to find out which values to pick for the lower quartile and the upper quartile.

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How To Find Quartiles in Excel (Plus Definition and FAQs) | Indeed.com

The result tells you the position that represents each quartile. For example, if the result is six for the lower quartile formula, the sixth number in your sequence is the lower quartile.

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Sometimes a "cut" is between two numbers ... the Quartile is the average of the two numbers.

Taylor & Francis Online

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Full article: Quartiles in Elementary Statistics

The most naive approach in defining quartiles is to think of the median as dividing the data set into halves (“bottom half” and “top half”) and then defining the lower (first) quartile Q1 to be the median of the bottom half, and the ...

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How to Find Quartiles in Even and Odd Length Datasets

December 21, 2022 - It follows this formula: Divide the data set into two halves, a bottom half and a top half. If n is odd, include the median value in both halves. Then the lower quartile is the median of the bottom half and the upper quartile is the median of ...

Statistics How To

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What are Quartiles? - Statistics How To

September 6, 2024 - Work the formula. There are 11 numbers, so: Q1 = ¼(n + 1)th Term. Q1 = ¼(11 + 1)th Term. Q1 = ¼(12)th Term. Q1 = 3rd Term. The lower quartile is the 3rd term (the 3rd place from the left): 1, 2, (Q1 = 4), 6, 7, 9, 12, 15, 18, 19, 27.

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Quartile Formula Explained with Examples - Testbook.com

The first quartile, also known as the lower quartile (Q1), is the middle value between the first term and the median. The third quartile, or upper quartile (Q3), is the middle value between the median and the last term.

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r/AskStatistics on Reddit: Question about Lower quartile, Upper quartile and IQR

March 31, 2024 -

Hey,

Today I was in a "Intro to statistics" course at my university and I think my lecturer made a mistake when she introduced us Q1, Q3 and IQR

This was the board:

This is the lecturer calculations. The data set is 1 to 14 as showed

From my understanding of "Lower quartile" is the median of the lower half, therefore Q1 should be 4

From my understanding of "Upper quartile" is the median of the upper half, therefore Q3 should be 11

I think my lecturer was wrong and IQR = 11- 4 = 7

Am I right?

Please explain it to me because I am very confused by this

Thanks!

Edit: I am so confused! both my casio fx-991ex CLASSWIZ and an online quartile calculator say Q1=4 and Q3=11 like I thought:

You are not right. Or, maybe you are. There are hundreds of different ways to define procedures for finding percentiles/quartiles. Here is a listing of some of the common ones you encounter. Therefore, it isn't really interesting to talk about "right" or "wrong" ways of finding them. However, in an intro stats course, make sure you understand the way your instructor wants you to use. One thing that is for certain is that this particular example used in this class is idiotic. It is pedagogically very important to separate the two ideas: The numbers representing the ranks of the data in order (1st, 2nd, 3rd, etc.), from The numbers in the data themselves. Confounding the two by using fake data that are the same as the rank orders is guaranteed to confuse 1/2 the students. In other words, in reality the 1st quartile isn't "(3+4)/2" in the example you provided, but the mean of the 3rd and 4th values in the data set ordered from smallest to largest.

From my understanding of "Lower quartile" is the median of the lower half, therefore Q1 should be 4 This is Tukey's definition of the hinges (which he then used in defining the boxplot). So yeah thats certainly a way to do it There's about 9 other ways to define a sample quantile that are common enough to have been used in stats programs. (Per Hyndman & Fan) If you scour textbooks you'll find one or two more. My daughter's school mathematics text from a few years ago has one I'd never seen before. So maybe it will be implemented somewhere and there will then be ten others in stats packages You need to find how it was defined in your course/textbook to see if rhe teacher is doing it that way or not.

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Range - Analysing data - Edexcel - GCSE Maths Revision - Edexcel - BBC Bitesize

February 13, 2023 - Lower quartile = \(\frac{7 + 1}{4}\) = \(\frac{8}{4}\), which is the second value in the list.

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statistics - How to calculate lower & upper quartiles? - Mathematics Stack Exchange

There are 24 values, and you have already ordered them. The 12th and 13th values are 5.00, so the median is indeed 5.00.

The lower quartile is indeed the median of the lower half. Since there are 12 numbers in the lower half, the median is the average of the 6th and the 7th one, which is exactly 1.745. If there were an odd number of items, you could simply take the middle one. (Typically the middle one of an even number of entries is taken to be the average of the two middle ones.)

I leave it to you to check that this method gives the answers you are supposed to get.

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Quartile Formula in Statistics: Examples, Interquartile Range, Template

September 20, 2023 - Let us calculate all the quartiles for it. ... First, find the median, i.e., the middle quartile (Q2) for the entire dataset. Then, divide the dataset into two equal groups. Now, find the median for the first group.

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