A confusing Q for beginners: Consider 6, 2, 4, 9, 1, 3, 5 as a population. Find the interquartile range.

[metinerol]

Hi!

I have just started to learn statistics and I had a quiz and I have done sth wrong. I would appreciate it if somebody can advise me the correct way to solve it.

The quiz question is below asks. One of them is the "interquartile range" which I have done wrong. (Other required data were correct so I don't mention them).

"THE QUESTION:

Consider the following data as a POPULATION.
6 , 2 , 4 , 9 , 1, 3 , 5
The interquartile range is .......... ; the mean is ............ ; the variance is............and the standard deviation is.............. (Record your answers correct to 4 decimal places.)"


I will try to explain what is confusing:

-Firstly, in excel I found Quartile 1 and Quartile 3, which were 2.5 and 5.5 respectively.
-Later, as interquartile range is basically difference between Q3 and Q1, therefore I found the result as 3 (5.5-2.5).
-However my answer was wrong.

When I searched a bit more in youtube, I realised that Interquartile range can also be calculated as such:

1 2 3 4 5 6 9

4 is in the middle...Therefore there are 2 groups except the middle 4, which are "1,2,3" and "5,6,9"....In Youtube after grouping numbers like that they find the difference between middle numbers of two groups, in our example 6-2 = 4

AS A RESULT, which is the interquartile range, 3 or 4 ?

Thank you for help!

 

[BigBeachBanana]

Hi!

I have just started to learn statistics and I had a quiz and I have done sth wrong. I would appreciate it if somebody can advise me the correct way to solve it.

The quiz question is below asks. One of them is the "interquartile range" which I have done wrong. (Other required data were correct so I don't mention them).

"THE QUESTION:

Consider the following data as a POPULATION.
6 , 2 , 4 , 9 , 1, 3 , 5
The interquartile range is .......... ; the mean is ............ ; the variance is............and the standard deviation is.............. (Record your answers correct to 4 decimal places.)"


I will try to explain what is confusing:

-Firstly, in excel I found Quartile 1 and Quartile 3, which were 2.5 and 5.5 respectively.
-Later, as interquartile range is basically difference between Q3 and Q1, therefore I found the result as 3 (5.5-2.5).
-However my answer was wrong.

When I searched a bit more in youtube, I realised that Interquartile range can also be calculated as such:

1 2 3 4 5 6 9

4 is in the middle...Therefore there are 2 groups except the middle 4, which are "1,2,3" and "5,6,9"....In Youtube after grouping numbers like that they find the difference between middle numbers of two groups, in our example 6-2 = 4

AS A RESULT, which is the interquartile range, 3 or 4 ?

Thank you for help!

How did you input it in to Excel?

 

[Dr.Peterson]

-Firstly, in excel I found Quartile 1 and Quartile 3, which were 2.5 and 5.5 respectively.
-Later, as interquartile range is basically difference between Q3 and Q1, therefore I found the result as 3 (5.5-2.5).
-However my answer was wrong.

When I searched a bit more in youtube, I realised that Interquartile range can also be calculated as such:
...
AS A RESULT, which is the interquartile range, 3 or 4 ?

There are different ways to define quartiles, as you have found, and therefore different answers for the IQR. You need to use whatever definition is given in your textbook, for your class. Don't go by what you find elsewhere, even if it is Excel!

I have seen two definitions called inclusive and exclusive IQR. For an explanation, see

Inclusive vs. Exclusive Interquartile Range | Psych Exam Review

psychexamreview.com

Apparently Excel does (sort of) support both, which I didn't know:

How to Find the Interquartile Range in Excel - Excel University

Did you know you can find the interquartile range in Excel in only 4 steps? See how to make an easy chart that calculates any dataset’s IQR!

www.excel-university.com

https://statisticsbyjim.com/basics/interquartile-range/

IQR - Exclusive or Inclusive, that is the question - Transfer Pricing Blog

I have spoken a lot about the arm’s length range and when we should use a statistical tool such as the interquartile range (IQR) to derive an arm’s length range. But how do we calculate the IQR practically? The easy answer is, Microsoft Excel or Numbers (for Mac) will do it for you, you just...

www.transferpricing.co.za

For more on the variability of quartiles, see

The Many Meanings of “Quartile” – The Math Doctors

www.themathdoctors.org

Several of these references point out that for real (large) data sets, the differences are unimportant; but for what I call "toy" data sets used in school, it matters what you use.

So, again, you should do the work by hand, using whatever method you were taught. What is that method?

 

[metinerol]

Thank you all...We havent learned the calculation of interquartile range....But somehow, a question appeared in the quiz...As my excel result was wrong, I assume the answer is expected to be found by using hand method. It is interesting to hear that there can be different results. Thanks again!

 

[metinerol]

How did you input it in to Excel?=QUART (array,1) = 1st quartile........QUART (array,3) =3rd Quartile....and I just deducted them.

 

[BigBeachBanana]

Thank you all...We havent learned the calculation of interquartile range....But somehow, a question appeared in the quiz...As my excel result was wrong, I assume the answer is expected to be found by using hand method. It is interesting to hear that there can be different results. Thanks again!

You're missing the point. The difference isn't the "hand" method or using Excel. The point here is that there are 2 methods of finding IQR i.e. Inclusive or Exclusive of the Median. That's why I asked how you input into Excel. The Excel University link provided by Dr.P above explained it clearly. I assumed you haven't looked at it.

 

[Dr.Peterson]

Thank you all...We havent learned the calculation of interquartile range....But somehow, a question appeared in the quiz...As my excel result was wrong, I assume the answer is expected to be found by using hand method. It is interesting to hear that there can be different results. Thanks again!

Interesting ... so you'll have to find out what method is taught there!

=QUART (array,1) = 1st quartile........QUART (array,3) =3rd Quartile....and I just deducted them.

Not only are there two methods for doing it by hand, there are (now) two methods in Excel! Apparently you used the old method -- except that I don't see that any version has a function called "QUART". It's always been QUARTILE.

Here is the help from my (current) version of Excel:

QUARTILE function​

Returns the quartile of a data set. Quartiles often are used in sales and survey data to divide populations into groups. For example, you can use QUARTILE to find the top 25 percent of incomes in a population.​

Important: This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.​

For more information about the new functions, see QUARTILE.EXC function and QUARTILE.INC function.​

Syntax​

QUARTILE(array,quart)​

The QUARTILE function syntax has the following arguments:​

• Array Required. The array or cell range of numeric values for which you want the quartile value.
• Quart Required. Indicates which value to return.

If quart equals​	QUARTILE returns​
0​	Minimum value​
1​	First quartile (25th percentile)​
2​	Median value (50th percentile)​
3​	Third quartile (75th percentile)​
4​	Maximum value​

​

Remarks​

• If array is empty, QUARTILE returns the #NUM! error value.
• If quart is not an integer, it is truncated.
• If quart < 0 or if quart > 4, QUARTILE returns the #NUM! error value.
• MIN, MEDIAN, and MAX return the same value as QUARTILE when quart is equal to 0 (zero), 2, and 4, respectively.

You are probably using a pre-2010 version.

Here are the two new functions:

QUARTILE.EXC function​

Returns the quartile of the data set, based on percentile values from 0..1, exclusive.​

Syntax​

QUARTILE.EXC(array, quart)​

The QUARTILE.EXC function syntax has the following arguments:​

• Array Required. The array or cell range of numeric values for which you want the quartile value.
• Quart Required. Indicates which value to return.

Remarks​

• If array is empty, QUARTILE.EXC returns the #NUM! error value.
• If quart is not an integer, it is truncated.
• If quart ≤ 0 or if quart ≥ 4, QUARTILE.EXC returns the #NUM! error value.
• MIN, MEDIAN, and MAX return the same value as QUARTILE.EXC when quart is equal to 0 (zero), 2, and 4, respectively.

and

QUARTILE.INC function​

Returns the quartile of a data set, based on percentile values from 0..1, inclusive.​

Quartiles often are used in sales and survey data to divide populations into groups. For example, you can use QUARTILE.INC to find the top 25 percent of incomes in a population.​

Syntax​

QUARTILE.INC(array,quart)​

The QUARTILE.INC function syntax has the following arguments:​

• Array Required. The array or cell range of numeric values for which you want the quartile value.
• Quart Required. Indicates which value to return.

Parameters​

If quart equals​	QUARTILE.INC returns​
0​	Minimum value​
1​	First quartile (25th percentile)​
2​	Median value (50th percentile)​
3​	Third quartile (75th percentile)​
4​	Maximum value​

Remarks​

• If array is empty, QUARTILE.INC returns the #NUM! error value.
• If quart is not an integer, it is truncated.
• If quart < 0 or if quart > 4, QUARTILE.INC returns the #NUM! error value.
• MIN, MEDIAN, and MAX return the same value as QUARTILE.INC when quart is equal to 0 (zero), 2, and 4, respectively.

I'm surprised how little they say about the difference! They seem to assume you'll be familiar with inclusive and exclusive IQR.

Anyway, when you find out what method you're expected to use (yes, by hand), it will probably be exclusive.