What Is The Median Of The Data Set? 24, 2, 13, 12, 2, 5, 10, 18 Enter Your Answer In The Box.

What is an Interquartile Range?

The interquartile range is a measure of where the "centre fifty" is in a data set up. Where a range is a measure out of where the starting time and stop are in a ready, an interquartile range is a measure of where the bulk of the values lie. That's why it'southward preferred over many other measures of spread when reporting things like school performance or SAT scores.

The interquartile range formula is the first quartile subtracted from the third quartile:

IQR = Q_three – Q_ane.

Watch the video for how to calculate the interquartile range by hand:

How to observe an interquartile range

Can't see the video? Click here.

Solve the formula by hand.

Steps:

Step 1: Put the numbers in order.
ane, two, five, half-dozen, 7, 9, 12, 15, eighteen, 19, 27.
Step ii: Detect the median.
one, two, 5, half-dozen, 7, ix, 12, 15, eighteen, 19, 27.
Step 3: Identify parentheses around the numbers higher up and below the median.
Not necessary statistically, just it makes Q1 and Q3 easier to spot.
(1, 2, 5, six, 7), 9, (12, 15, 18, xix, 27).
Step 4: Find Q1 and Q3
Remember of Q1 every bit a median in the lower half of the data and recall of Q3 as a median for the upper one-half of data.
(1, 2, 5, half-dozen, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.
Step five: Subtract Q1 from Q3 to observe the interquartile range.
18 – 5 = 13.

Similar the explanation? Check out the Practically Adulterous Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!

What if I Have an Fifty-fifty Set of Numbers?

Example question: Discover the IQR for the following data gear up: 3, v, 7, 8, 9, 11, xv, 16, 20, 21.

Footstep ane: Put the numbers in order.
three, 5, vii, 8, ix, 11, 15, xvi, xx, 21.
Stride two: Make a marker in the center of the data:
3, 5, vii, 8, 9, | 11, fifteen, 16, 20, 21.
Footstep 3: Place parentheses effectually the numbers above and below the marker you made in Step 2--it makes Q1 and Q3 easier to spot.
(3, v, 7, eight, 9), | (11, 15, xvi, 20, 21).
Footstep 4: Observe Q1 and Q3
Q1 is the median (the eye) of the lower half of the data, and Q3 is the median (the center) of the upper half of the data.
(three, 5, vii, eight, ix), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.
Footstep 5: Subtract Q1 from Q3.
16 – vii = nine.
This is your IQR.

Find an interquartile range for an odd set of numbers: Alternate Method

As you may already know, cypher is "set in stone" in statistics: when some statisticians detect an interquartile range for a set of odd numbers, they include the median in both both quartiles. For example, in the following ready of numbers: one, 2, 5, 6, 7, 9, 12, xv, 18, 19, 27 some statisticians would intermission it into ii halves, including the median (9) in both halves:
(one, ii, 5, 6, 7, nine), (9, 12, 15, xviii, 19, 27)
This leads to two halves with an even set of numbers, so you can follow the steps in a higher place to find the IQR.
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Box Plot interquartile range: How to observe it

Lookout man the video for the steps.

How to find an interquartile range on a boxplot

Tin't see the video? Click here.

Box Plot interquartile range: How to notice it

box plot interquartile range

Instance question: Find the interquartile range for the higher up box plot.

Step 1: Find Q1.Q1 is represented by the left mitt edge of the "box" (at the point where the whisker stops).

In the above graph, Q1 is approximately at two.vi. (A complete explanation of Q1 is here: The five number summary.)
Footstep 2: Find Q3.
Q3 is represented on a boxplot by the correct hand edge of the "box".

Q3 is approximately 12 in this graph.
Pace 3: Subtract the number you lot establish in pace ane from the number you lot found in step 3.
This volition requite you lot the interquartile range. 12 – ii.vi = 9.iv.

That'south it!

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Interquartile Range in Minitab

Lookout the video for stride-by-step directions:

How to find an interquartile range in Minitab

Tin can't see the video? Click hither.

Interquartile Range in Minitab: Steps

Example question: Find an interquartile range in Minitab for the Course Point Boilerplate (GPA) in the following data ready:
Course Betoken Average (GPA): 1(three.2), i(3.one), 2(3.five), 2(2.0), 3(1.9), iii(4.0), 3(3.9), 4(3.8), 4(2.nine), 5(three.ix), v(iii.2), five(iii.3), vi(3.four), 6(ii.6), 6(two.v), seven(2.0), 7(1.5), 8(4.0), 8(two.0).

Step 1: Type your information into a Minitab worksheet. Enter your information into one or two columns.
minitab interquartile range a

Footstep 2: Click "Stat," then click "Basic Statistics," then click "Display Descriptive Statistics" to open the Descriptive Statistics menu.
minitab interquartile range b

Stride three: Click a variable name in the left window and and then click the "Select" push to transfer the variable name to the correct-hand window.

Footstep 4: Click the "Statistics" button.
minitab interquartile range c

Pace v: Cheque "Interquartile Range."
minitab interquartile range d .

Step half-dozen: Click the "OK" push button (a new window will open with the consequence). The IQR for the GPA in this particular data set is 1.8.
minitab interquartile range e

That's it!

Tip: If you don't see descriptive statistics bear witness in a window, click "Window" on the toolbar, then click "Tile." Click the Session window (this is where descriptive statistics appear) and then scroll up to see your results.

Interquartile Range in Excel 2007

How to Find an Interquartile Range Excel 2007

Picket the video or read the steps below to find an interquartile range in Excel 2007:

How to find an interquartile range in Excel

Steps:
Step i: Enter your information into a single Excel column on a worksheet. For instance, type your data in cells A2 to A10. Don't leave whatsoever gaps in your data.

Step 2: Click a blank cell (for case, click cell B2) and then blazon =QUARTILE(A2:A10,one). You lot'll demand to supplant A2:A10 with the bodily values from your data set. For instance, if you typed your data into B2 to B50, the equation is =QUARTILE(B2:B50,ane). The "one" in this Excel formula(A2:A10,1) represents the kickoff quartile (i.due east the signal lying at 25% of the data set).

Pace 3: Click a second blank prison cell (for example, click cell B3) and and then type =QUARTILE(A2:A10,3). Replace A2:A10 with the bodily values from your data set. The "3" in this Excel formula (A2:A10,3) represents the 3rd quartile (i.e. the point lying at 75% of the information ready).

Step four: Click a third blank cell (for case, click cell B4) and and then type =B3-B2. If your quartile functions from Step 2 and 3 are in dissimilar locations, change the prison cell references.

Step 5: Press the "Enter" key. Excel will return the IQR in the cell you lot clicked in Stride four

That's it!

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How to Find an Interquartile Range in SPSS

Like well-nigh technology, SPSS has several ways that you tin can calculate the IQR. However, if yous click on the near intuitive way y'all would wait to find information technology ("Descriptive Statistics > Frequencies"), the surprise is that it won't list the IQR (although information technology volition list the first, second and third quartiles). You could take this route and then subtract the third quartile from the beginning to become the IQR. However, the easiest way to find the interquartile range in SPSS by using the "Explore" command. If you have already typed data into your worksheet, skip to Pace 3.

Spotter the video for the steps:

How to notice the Interquartile Range in SPSS

Tin't encounter the steps? Click hither.

Steps

Step i: Open up a new information file in SPSS. Click "File," mouse over "New" and then click "Information."

Stride two: Type your data into columns in the worksheet. Y'all can utilise as many columns equally yous need, but don't go out blank rows or spaces between your data. Encounter: How to Enter Data into SPSS.

Step three: Click "Analyze," and then mouse over "Descriptive Statistics." Click "Explore" to open up the "Explore" dialog box.
how to find the interquartile range in SPSS 1

Step 4: Click the variable proper name (that's simply a fancy name for the column heading), and then click the top arrow to move the variable into the "Dependent list" box.

The "Explore" variables dialog box.

Footstep v: Click "OK." The interquartile range is listed in the Descriptives box.
interquartile range SPSS 3

Tip: This example has only 1 listing typed into the data sheet, only y'all may have several to choose from depending on how yous entered your information. Brand certain you select the right variable (column names) earlier proceeding. If you desire more than memorable variable names, change the column title by clicking the "variable view" button at the very bottom left of the worksheet. Type in your new variable name and so return to data view by clicking the "information view" button.
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What is an Interquartile Range?

Imagine all the data in a set as points on a number line. For example, if y'all have 3, 7 and 28 in your gear up of data, imagine them every bit points on a number line that is centered on 0 but stretches both infinitely below zero and infinitely above naught. One time plotted on that number line, the smallest data point and the biggest data point in the set of data create the boundaries (i.due east. a lower bound and an upper leap) of an interval of space on the number line that contains all information points in the ready. The interquartile range (IQR) is the length of the heart 50% of that interval of space.

what is an interquartile range

The interquartile range is the middle 50% of a data ready. Box and whiskers image past Jhguch at en.wikipedia

If y'all want to know that the IQR is in formal terms, the IQR is calculated every bit: The difference between the third or upper quartile and the commencement or lower quartile. Quartile is a term used to describe how to divide the set of data into four equal portions (think quarter).

IQR Example

If yous have a set up containing the data points 1, 3, 5, 7, 8, 10, 11 and 13, the first quartile is 4, the second quartile is 7.5 and the third quartile is 10.5. Draw these points on a number line and you'll see that those iii numbers split up the number line in quarters from 1 to xiii. As such, the IQR of that data set is half dozen.5, calculated equally 10.v minus 4. The offset and third quartiles are also sometimes chosen the 25th and 75th percentiles considering those are the equivalent figures when the information set is divided into percents rather than quarters.

Interquartile Range using the TI83

Spotter the video for the steps:

TI 83 Interquartile Range

Can't see the video? Click here.

While yous can utilise the dandy online interquartile range calculator on this website, that might non be an option in a quiz or test. Well-nigh instructors allow the use of a TI-83 on tests, and it's even 1 of the few calculators allowed in the AP Statistics examination. Finding the TI 83 interquartile range involves naught more than entering your data list and pushing a couple of buttons.

Example problem: Detect the TI 83 interquartile range for the heights of the top 10 buildings in the world (as of 2009). The heights, (in feet) are: 2717, 2063, 2001, 1815, 1516, 1503, 1482, 1377, 1312, 1272.

Steps

Step 1: Enter the higher up data into a list on the TI 83 calculator. Press the STAT button and then press ENTER. Enter the outset number (2717), and then press ENTER. Continue entering numbers, pressing ENTER subsequently each entry.

Pace 2: Press the STAT push button.

Step 3: Press the correct arrow button (the arrow keys are located at the acme correct of the keypad) to select "Calc."

Footstep iv: Press ENTER to highlight "1-Var Stats."

Step 5: Press ENTER again to bring upwardly a list of stats.

Step 6: Scroll down the list with the arrow keys to notice Q1 and Q3. Write those numbers down. You could copy and paste the numbers but unfortunately, Texas Instruments doesn't make this easy:

Use the pointer keys to identify the cursor at the beginning of the
text that yous want to highlight.
Using the TI Keyboard, press and agree down the Shift key, and then apply the arrow keys to highlight the text.
Release the Shift primal and arrow fundamental.

The re-create and paste menu should appear, enabling you to re-create and paste the data. You would take to do this twice (returning to the Domicile screen each time), and then information technology'south much faster just to write the numbers down.

Step 7:Subtract Q1 from Q3 to find the IQR (strong>624 feet for this set up of numbers).

That's it!
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How to Detect Q1, Q3 and the Interquartile Range TI 89

Example problem: Observe Q_one, Q₃, and the IQR for the post-obit list of numbers: 1, 9, two, three, 7, 8, 9, ii.

Step i: Printing APPS. Scroll to Stats/List Editor (apply the pointer keys on the keypad to ringlet). Press ENTER. If you don't have the stats/list editor y'all can download information technology here.

Stride 2: Clear the list editor of data: press F1 8.

Step 3: Press Alpha 9 ALPHA 1 ENTER. This names your list "IQ."

Step 4: Enter your numbers, i at a fourth dimension. Follow each entry by pressing the ENTER cardinal. For our grouping of numbers, enter
1,9,2,3,7,viii,9,2

Step five: Press F4, then ENTER (for the ane-var stats screen).

Step half-dozen: Tell the figurer you want stats for the list called "IQ" by entering Blastoff nine Blastoff 1 into the "List:" box. The reckoner should automatically put the cursor there for yous. Press ENTER twice.

Step seven: Read the results. Q_i is listed as Q1X (in our example, Q1X=2). Q₃ is listed as Q3X (Q3X=8.5). To find the IQR, subtract Q_one from Q_iii on the Home screen. The IQR is 8.5-2=6.5.

That's it!

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What is The Interquartile Range Formula?

The IQR formula is:
IQR = Q₃ – Q₁

Where Q₃ is the upper quartile and Q₁ is the lower quartile.

the interquartile range formula

IQR as a test for normal distribution

Use the interquartile range formula with the hateful and standard deviation to test whether or not a population has a normal distribution. The formula to make up one's mind whether or non a population is normally distributed are:
Q_i – (σ z₁) + Ten
Q_three – (σ z₃) + X
Where Q₁ is the showtime quartile, Q₃ is the third quartile, σ is the standard difference, z is the standard score ("z-score") and Ten is the hateful. In order to tell whether a population is normally distributed, solve both equations then compare the results. If at that place is a significant difference between the results and the first or tertiary quartiles, then the population is not normally distributed.

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What is an Interquartile Range Used For?

The IQR is used to measure how spread out the data points in a set are from the mean of the data set. The higher the IQR, the more spread out the data points; in dissimilarity, the smaller the IQR, the more bunched upwards the data points are around the mean. The IQR range is one of many measurements used to mensurate how spread out the data points in a data gear up are. It is best used with other measurements such every bit the median and total range to build a complete motion-picture show of a data ready's tendency to cluster around its mean.
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Where Does the term Interquartile Range Come From?

Who invented the term "Interquartile Range?" In order to notice that out, we have to get back to the 19th century.

History

British dr. Sir Donald MacAlister used the terms lower quartile and higher quartile in the 1879 publication, the Law of the Geometric Mean. Proc. R. Soc. XXIX, p. 374: " "Equally these two measures, with the mean, divide the curve of facility into four equal parts, I propose to call them the 'higher quartile' and the 'lower quartile' respectively."
origin of the word quartile

Although a physician by trade, he was gifted with mathematics and accomplished the highest score in the final mathematics exams at Cambridge University in 1877. He spoke xix languages including English, Czech and Swedish.

Macalister'southward paper, the Law of the Geometric Mean was actually in response to a question put forward by Francis Galton (inventor of the Galton board). All the same, information technology wasn't until 1882 that Galton ("Report of the Anthropometric Commission") used the upper quartile and lower quartile values and the term "interquartile range" —defined as twice the probable mistake. Galton wasn't just a statistician—he was also an anthropologist, geographer, proto-genetecist and psychometrician who produced more than 340 books. He also coined the statistical terms "correlation" and "regression toward the hateful."

References

Gonick, Fifty. and Smith, W. The Cartoon Guide to Statistics. New York: Harper Perennial, pp. 20-21, 1993.

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