**The**re **are** **a** v**a**riety **of** descriptive st**a**tistics. **Numbers** such **as** **the** me**a**n, medi**a**n , mode, skewness , kurtosis, st**a**nd**a**rd devi**a**tion , first qu**a**rtile **a**nd third qu**a**rtile, to n**a**me **a** few, e**a**ch tell us something **a**bout our d**a**t**a**. R**a****the**r th**a**n looking **a**t **thes**e descriptive st**a**tistics individu**a**lly, sometimes combining **the**m helps to give us **a** complete picture. With this end in mind, **the** **five**-**number** **summary** is **a** convenient w**a**y to combine **five** descriptive st**a**tistics.

It is cle**a**r **that** **the**re **are** to be **five** **numbers** in our **summary**, but **which** **five**? **The** **numbers** chosen **are** to help us know **the** center **of** our d**a**t**a**, **as** well **as** how spre**a**d out **the** d**a**t**a** points **are**. With this in mind, **the** **five**-**number** **summary** consists **of** **the** **following**:

**The**minimum – this is**the**sm**a**llest v**a**lue in our d**a**t**a**set.**The**first qu**a**rtile – this**number**is denoted*Q*1**a**nd 25%**of**our d**a**t**a**f**alls**below**the**first qu**a**rtile.**The**medi**a**n – this is**the**midw**a**y point**of****the**d**a**t**a**. 50%**of****a**ll d**a**t**a**f**alls**below**the**medi**a**n.**The**third qu**a**rtile – this**number**is denoted*Q*3**a**nd 75%**of**our d**a**t**a**f**alls**below**the**third qu**a**rtile.**The**m**a**ximum – this is**the**l**a**rgest v**a**lue in our d**a**t**a**set.

**The** me**a**n **a**nd st**a**nd**a**rd devi**a**tion c**a**n **a**lso be used toge**the**r to convey **the** center **a**nd **the** spre**a**d **of** **a** set **of** d**a**t**a**. However, both **of** **thes**e st**a**tistics **are** susceptible to outliers. **The** medi**a**n, first qu**a**rtile, **a**nd third qu**a**rtile **are** not **as** he**a**vily influenced by outliers.

Given **the** **following** set **of** d**a**t**a**, we will report **the** **five** **number** **summary**:

1, 2, 2, 3, 4, 6, 6, 7, 7, 7, 8, 11, 12, 15, 15, 15, 17, 17, 18, 20

**The**re **are** **a** tot**a**l **of** twenty points in **the** d**a**t**as**et. **The** medi**a**n is thus **the** **a**ver**a**ge **of** **the** tenth **a**nd eleventh d**a**t**a** v**a**lues or:

(7 + 8)/2 = 7.5.

**The** medi**a**n **of** **the** bottom h**a**lf **of** **the** d**a**t**a** is **the** first qu**a**rtile. **The** bottom h**a**lf is:

1, 2, 2, 3, 4, 6, 6, 7, 7, 7

Thus we c**a**lcul**a**te*Q* 1 = (4 + 6)/2 = 5.

**The** medi**a**n **of** **the** top h**a**lf **of** **the** origin**a**l d**a**t**a** set is **the** third qu**a**rtile. We need to find **the** medi**a**n **of**:

8, 11, 12, 15, 15, 15, 17, 17, 18, 20

Thus we c**a**lcul**a**te*Q* 3 = (15 + 15)/2 = 15.

We **as**semble **a**ll **of** **the** **a**bove results toge**the**r **a**nd report **that** **the** **five** **number** **summary** for **the** **a**bove set **of** d**a**t**a** is 1, 5, 7.5, 12, 20.

**Five** **number** summ**a**ries c**a**n be comp**are**d to one **a**no**the**r. We will find **that** two sets with **the** simil**a**r me**a**ns **a**nd st**a**nd**a**rd devi**a**tions m**a**y h**a**ve very different **five** **number** summ**a**ries. To e**as**ily comp**are** two **five** **number** summ**a**ries **a**t **a** gl**a**nce, we c**a**n use **a** boxplot , or box **a**nd whiskers gr**a**ph.

A summary consists of five values: **the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median**. more

Discovered by mathemagician Srinivas Ramanujan, 1729 is said to be the magic number because it is **the sole number which can be expressed as the sum of the cubes of two different sets of numbers**. more

- When selecting separate words throughout a web page, you can **double-click while holding ctrl instead of dragging to select**. - When making overlapping selections, ctrl+z will remove the combined selection. more

- Step 1: Specify the set of options.
- Step 2: Decide whose costs and benefits count.
- Step 3: Identify the impacts and select measurement indicators.
- Step 4: Predict the impacts over the life of the proposed regulation.
- Step 5: Monetise (place dollar values on) impacts.

Terms in this set (5) Which of he following is not part of a five-number summary? **The mean**. more

Cyber Definitions Beginning with Numbers more

*Source: www.thoughtco.com*

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