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Understanding Quartiles: Definitions, Calculations, and Examples

August 3, 2025 - The median of their scores would be the arithmetic average of the tenth and eleventh numbers in the above example if you had 20 students instead of 19. The best way is to use a spreadsheet and the QUARTILE function.

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How to Calculate the Upper Quartile: 13 Steps (with Pictures)

May 6, 2024 - Make sure you include a comma after ... the upper quartile of cells A1 through A10, your function will look like this: =(QUARTILE(A1:A10, 3))....

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

Find the Lower Quartile and Upper Quartile - YouTube

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September 30, 2023

Understanding the Upper Quartile | Math with Mr. J - YouTube

Lesson 23 - Quartiles Of Data Explained (Statistics Tutor) - YouTube

Find the Median, Lower Quartile, and Upper Quartile - YouTube

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How do you find the upper quartile?

The upper quartile can found either by using the median method or the upper quartile formula. The median method is finding the median, then finding the upper quartile as the middle of the last half of the data set. The upper quartile formula uses the amount of terms in the data set, adding 1, multiplying by 3 (upper/third quartile), then dividing by four (quartiles); this gives the term number.

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Upper Quartile | Definition. Formula & Examples - Lesson | Study.com

How do you write upper and lower quartiles?

The lower quartile is the number in the middle between the lower extreme or minimum and the median. It is written as a single data point using the lower quartile symbol. The upper quartile is the number in the middle between the median and the upper extreme or maximum. It is written as a single data point using the upper quartile symbol.

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Upper Quartile | Definition. Formula & Examples - Lesson | Study.com

How do I find quartiles in R?

You can use the quantile() function to find quartiles in R. If your data is called “data”, then “quantile(data, prob=c(.25,.5,.75), type=1)” will return the three quartiles.

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Quartiles & Quantiles | Calculation, Definition & Interpretation

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Upper Quartile | Definition. Formula & Examples - Lesson | Study.com

October 30, 2015 - If the result from the formula ... term found from the formula. For example, if the result is 7.5, then the average of the 7th and 8th terms in the data set is the upper quartile....

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Quartile Calculator | Interquartile Range Calculator

The lower quartile Q1 is the median of the lower half of the data. The upper quartile Q3 is the median of the upper half of the data.

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Quartiles & Quantiles | Calculation, Definition & Interpretation

June 21, 2023 - Just type “lower quartile x,y,z” to calculate the lower quartile of your data set, or “upper quartile x,y,z” for the upper quartile of your data set.

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+3) data points, ... the upper quartile is 25% of the (3n+2)th data point plus 75% of the (3n+3)th data point. ... Another way to explain this method is that we are finding a rank within the data, which can then be used to determine ...

Computing methods

Computer software for quartiles

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How To Calculate the Upper Quartile of a Dataset in 3 Steps | Indeed.com

For example, consider a coach who records the following 100-meter sprint times for eight high school football players in seconds: {13.4, 13.6, 14.0, 14.5, 15.2, 16.8, 17.6, 19.1}. A college scout realizes it's unfair to compare the sprint time ...

Published June 27, 2024

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

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What are Quartiles? - Statistics How To

September 6, 2024 - You may also want to use the formula if you are uncomfortable with finding the median for sets of data with odd or even numbers. Example question: Find the upper quartile for the following set of numbers: 27, 19, 5, 7, 6, 9, 15, 12, 18, 2, 1.

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Upper Quartile - an overview | ScienceDirect Topics

So, for example, if the upper quartile of the first group is 12 and the upper quartile of the second group is 8, we can say that the typical individual in the high end of the first group is better off than the comparable person in the second group. Of course, there is nothing sacred about the ...

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Quartile - Math Steps, Examples & Questions

January 13, 2025 - Drawing a horizontal line from the cumulative frequency axis at the value 60.25, across to the curve and then down to the x -axis, the upper quartile is approximately 42{~m} (see diagram below).

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Quartile Formula - What is Quartile Formula?

Solution: The upper quartile (18) is the 9th term or on the 9th place from the left. Example 3: Find the 3rd quartile in the following data set: 4, 5, 8, 7, 11, 9, 9

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Flexi answers - How do I find the lower quartile and upper quartile? | CK-12 Foundation

September 11, 2025 - The median of the second half of the data is called the upper quartile. The procedure for determining quartiles involves utilizing a series of steps, which can be demonstrated through an example. Here is a data set from a survey of the number of hours worked by teenagers with part-time jobs.

Statistics Canada

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4.5.1 Calculating the range and interquartile range

The lower quartile is the mean ... is the mean of the values of data point of rank 6 + 3 = 9 and the data point of rank 6 + 4 = 10, which is (43 + 47) ÷ 2 = 45....

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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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What is the upper quartile in math? - Quora

Answer (1 of 2): Upper quartile ... the upper quartile by using the following firmula: (1) Individual Series:- Upper Quartile =( 3/4)(n+1)th. term or 75% of (n+1)th.term E.g.:- Ar......

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Upper Quartile - Statistics By Jim

May 17, 2025 - Values that fall well above Q3 may be considered unusually high. For example, if a dataset of test scores has an upper quartile of 88, that means 75% of students scored 88 or lower, and 25% scored higher.

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MathCS: Intro to Statistics with Excel

Similarly, the upper quartile can be shown to be 4. For larger data sets, the quartiles can be selected as follows: Examples: Find the quartiles for the values 1, 2, 3, 4, 5, 6, 7 and also for the values 1, 2, 3, 4, 5 using this new method.