five number theory

8/13/2019 Five Number Theory

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1) Range:The range of a set of numbers is found by computing the difference

between the highest score and the lowest score. For example, the range of the

following set of data:

34 ! "1 ## $$ %" 1 "% 44 #4 &&

is 99 - 15 = 84

%) Median:The median is the middle 'alue of a set of numbers when the numbers

are arranged in either ascending or descending order. The median separates thedata into two e(ual hal'es !* of the numbers are below the median, !* of the

numbers are abo'e the median. +f there is an e'en number of 'alues, the median is

the mean of the two middle 'alues.

For example, consider the set of numbers we used abo'e in the range example.

First, arrange them in order:

1 %" 34 44 ! "1 "% #4 ## && $$

ow, find the middle 'alue. -ne simple way is ust to start counting at both ends,

crossing out a number at each end until you arri'e at the middle 'alue.

/ formula way of arri'ing at the middle term is this:

middle term 0 2 1) % , where 0 the number of 'alues. +n this example, 011, so

middle term 0 11 2 1) %which is 1% %, or ". o the middle term will be the "th term, which correlates to

the 'alue 61. Therefore, 61is the median.

ow, suppose there is an e'en number of 'alues. 5onsider the following set of

numbers.

1& 1 11 14 1% 1# 1" 14 1# 13

there are 1! 'alues. /rranged in order, they loo6 li6e this:

11 1% 13 14 14 1 1" 1# 1# 1&

7owe'er, there is no exactmiddle term. +t would fall between the second number

14 the fifth term) and the number 1 the sixth term). Therefore, the median

would be the mean of the two terms, or 14.5.

3) First Quartile: The first (uartile of a set of numbers is the 'alue in which %*


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of the numbers are below it, #* of the numbers are abo'e it when the numbers

are arranged in ascending increasing) order.

Third Quartile:The third (uartile of a set of numbers is the 'alue in which #*

of the numbers are below it, %* of the numbers are abo'e it when the numbers

are arranged in ascending increasing) order.

/nother way to thin6 of the (uartiles is this: The first (uartile is the median of the

numbers located belowthe median the third (uartile is the median of thenumbers aboethe median. This may sound confusing, but it is easy to understand

once a few examples are used:

For instance, loo6 at the first set of numbers we used, arranged in ascending order.

8emember "1 is the median. ote how the median "1) di'ides the numbers into

two e(ual groups:

1 %" 34 44 ! 61 "% #4 ## && $$

The numbers below the median are 1 %" 34 44 !. The median middle

'alue) of those numbers is !4. o, !4is the first (uartile. imilarly, the numbers

abo'e the median are "% #4 ## && $$. The median middle 'alue) of those

numbers is "". o, ""is the third (uartile.

7ighlighting each (uartile and the median, you can see how they di'ide the

numbers into four e(ual groups:

1 %" !4 44 ! 61 "% #4 "" && $$

The second set of data we used, arranged in order, loo6ed li6e this. 8emember, themedian of this set was not a number in the set rather it was a number between two

other numbers 14.5 = #).

11 1% 13 14 14 # 1 1" 1# 1# 1&

o, the numbers below the median, 11 1% 13 14 14, ha'e a median of 1!. o,the first (uartile is 1!. The numbers abo'e the median, 1 1" 1# 1# 1&, ha'e

a median of 1"the first one). o, the third (uartile is1".

/gain, highlighting each (uartile and the median, you can see how they di'ide the

numbers into four e(ual groups:

11 1% 1! 14 14 # 1 1" 1" 1# 1&

4) Fie nu$ber su$$ar%: / fi'e number summary consists of these fi'estatistics: the minimum 'alue, the first (uartile, the median, the third (uartile, and


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the maximum 'alue of a set of numbers. For the two groups of numbers abo'e, the

fi'e number summary is:

1st data

set

%nd data

set

9inimum: 1 11

First uartile: 34 13

9edian: "1 14.

Third

uartile:## 1#

9aximum: $$ 1&

/ &o' (lotis a graphical representation of a fi'e number summary. The ends of

the ;box; are the first and third (uartiles, with the median inside the ;box;.

five number theory

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