How To Find Quartiles In A Data Set

Contents:

1. Quartiles: Definition, Finding
2. What is an Upper Quartile?
3. Quartile Role Excel
4. Deviation between a quarter and a quartile

What are Quartiles? Definition

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Quartiles are values that divide your data into quarters. Still, quartiles aren't shaped like pizza slices; Instead they split up your information into 4 segments according to where the numbers fall on the number line. The four quarters that divide a data prepare into quartiles are:

1. The lowest 25% of numbers.
2. The next everyman 25% of numbers (up to the median).
3. The second highest 25% of numbers (above the median).
4. The highest 25% of numbers.

As quartiles divide numbers upward co-ordinate to where their position is on the number line, you accept to put the numbers in lodge before you can figure out where the quartiles are.

Detect Quartiles: Examples

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Instance: Divide the following data prepare into quartiles: 2, 5, 6, 7, 10, 22, 13, xiv, sixteen, 65, 45, 12.

Step 1: Put the numbers in order: ii, five, 6, vii, 10, 12 13, xiv, 16, 22, 45, 65.
Step 2: Count how many numbers in that location are in your set and then split up by 4 to cut the listing of numbers into quarters. There are 12 numbers in this set, and so yous would accept 3 numbers in each quartile.
2, 5, 6, | vii, x, 12 | thirteen, 14, sixteen, | 22, 45, 65

If you have an uneven set of numbers, information technology's OK to slice a number downward the centre. This can get a trivial tricky (imagine trying to split ten, xiii, 17, 19, 21 into quarters!), and then you lot may want to use an online interquartile range calculator to figure those quartiles out for you. The calculator gives y'all the 25th Percentile, which is the end of the first quartile, the 50th Percentile which is the end of the 2d quartile (or the median) and the 75th Percentile, which is the end of the 3rd quartile. For 10, 13, 17, 19 and 21 the results are:
25th Percentile: 11.5
50th Percentile: 17
75th Percentile: twenty
Interquartile Range: eight.v.

Why do we need quartiles in statistics? The main reason is to perform further calculations, similar the interquartile range, which is a measure out of how the data is spread out effectually the mean.

What is an Upper Quartile?

The upper quartile (sometimes called Q3) is the number dividing the tertiary and 4th quartile. The upper quartile can as well be thought of as the median of the upper half of the numbers. The upper quartile is besides called the 75th percentile; it splits the everyman 75% of data from the highest 25%.

A set of numbers (-3,-2,-ane,0,one,ii,3) divided into four quartiles.

Computing the Upper Quartile

You can detect the upper quartile past placing a fix of numbers in order and working out Q3 by hand, or you can use the upper quartile formula. If yous have a small-scale fix of numbers (under well-nigh 20), past mitt is ordinarily the easiest choice. Notwithstanding, the formula works for all sets of numbers, from very modest to very large. You may as well want to use the formula if y'all are uncomfortable with finding the median for sets of data with odd or even numbers.

Example question: Detect the upper quartile for the following set of numbers:
27, xix, 5, seven, 6, nine, xv, 12, eighteen, 2, 1.

By Hand

Step 1: Put your numbers in order: i, 2, v, vi, seven, 9, 12, fifteen, 18, nineteen, 27
Step ii: Find the median: one, two, 5, 6, 7, 9, 12, xv, 18, 19, 27.
Stride 3: Identify parentheses effectually the numbers in a higher place the median.
1, 2, v, 6, 7, nine, (12, 15, 18, 19, 27).
Pace 4: Find the median of the upper set of numbers. This is the upper quartile:
1, 2, 5, six, vii, 9, (12, 15, 18 ,19 ,27).

Using the Formula

The upper quartile formula is:
Q_iii = ¾(n + ane)^th Term.
The formula doesn't give you the value for the upper quartile, information technology gives you the place. For case, the 5th identify, or the 76th place.
Stride 1: Put your numbers in club: i, two, 5, vi, 7, 9, 12, 15, 18, 19, 27.
Annotation: for very large data sets, you may want to use Excel to identify your numbers in order. Run into: Sorting Numbers in Excel.
Footstep two: Work the formula. There are 11 numbers in the fix, so:
Q₃ = ¾(n + 1)^th Term.
Q_iii = ¾(11 + 1)^th Term.
Q₃ = ¾(12)^th Term.
Q₃ = 9^th Term.
In this set of numbers (1, 2, v, half dozen, 7, ix, 12, 15, 18, 19, 27), the upper quartile (18) is the 9th term, or the 9th place from the left.

Quartile Role Excel

Y'all can as well find a quartile in Microsoft Excel using the Excel quartile function.

1. Type your data into a single cavalcade. For example, type your data into cells A1 to A10.
2. Click an empty cell somewhere on the canvass. For example, click cell B1.
3. Blazon "=QUARTILE(A1:A10,i)" and and then press "Enter". This finds the first quartile. To notice the third quartile, blazon "=QUARTILE(A1:A10,3)".
   Note: If your data is in a different jail cell range other than A1:A10, make sure yous change the function to reflect that.

Deviation between a quarter and a quartile

There'due south a slight difference between a quarter and quartile. A quarter is the whole slice of pizza, but a quartile is the marker the pizza cutter makes at the cease of the slice.

A quarter of the pizza is the whole slice; a quartile marks the end of the first quarter and the outset of the second.

References

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, South.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Lindstrom, D. (2010). Schaum's Easy Outline of Statistics, 2nd Edition (Schaum'southward Easy Outlines) 2nd Edition. McGraw-Hill Pedagogy

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How To Find Quartiles In A Data Set,

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