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Wednesday, March 15, 2006 

Statistics

Hey! Sorry that I only gotten this posted up now. Ah, I know its late already too. So today we had two math classes and in the first math class we started writing our notes on statistics in our dictionaries. So for anyone who missed the day here it is!

Statistics

statistics: the branch of mathematics that deals with collecting, organizing, displaying, and analyzing.

statistic: a number that describes one aspect of a group of data.
EXAMPLE: mean, median, mode, range, standard deviation, etc...

datum: one bit (piece) of information.
data: many bits (pieces) of information.


the "flavors" of data
guantitative data and qualitative date

quantitative data

data that is numeric
(eg. height, weight, time..)

there are two kinds of quantitative date
continuous and discrete

continuous - can be represented using real numbers (eg. height, weight, time, etc..)

discrete - can be represented by using ONLY intergers (eg. # of people, # of cars, # of animals, etc..)

qualitative date

data that is non-numeric
(eg. colours, flavours, etc...)


measures of central tendency

mean: ( A.K.A. 'the arithmetic mean") the symbol of mean is an x with a line RIGHT on top. ( i couldnt find it on character map so this will have to do x¯, sorry! )
- the arithmetic average oof a set of values.

x¯ = Σx/n


where the x¯ with the line RIGHT on top is the mean
where Σx means the sumer of all data (x) in the set (Σ - is called sigma)
where n is the number of data in a set

EXAMPLE: find the average mark this set of 5 quizzes.
48,52,65,45,65.

Σx/n = 48+52+65+45+65/5
=275/5
=55

median ( med) : 1) the middle value in an ordered ( say from smallest to largest) set of data.
2) if there are an even number of data, the median is the average of the middle pair in an ordered set of data.

EXAMPLE: find the median of these quiz scores:
12,10,17,11,15
SOLUTION: 10, 11, 12, 15, 17
12 is the median.

EXAMPLE: find the median of these scores:
12,10,17,11,15,11
SOLUTION: 10,11,11,12,15,17
(11+12)/2 =23/2
=11.5
the median is 11.5

mode (mo): the datum that occures most frequently in a set of data.

EXAMPLE: find the mode in the set of quiz scores:
12,10,17,11,15,11
SOLUTION: the mode is 11 because it occurs more often that any other number in the set.

measures of variability
determine how "spread out" or varied" a set of data is.

range: the difference between the largest and smallest value in a set of data.

EXAMPLE: find the range of ages of people in our class

17,17,18,17,16,17,18,18,18,17,17,18,18,17,18,19,18,19


highest value: 19
lowest value: 16
RANGE: 19-16=3

with teacher MR K.-38 yrs old.
highest value: 38
lowest value: 16
RANGE: 38-16=22

standard deviation: σ represents the "population standard deviation"
S represents the "sample standard deviation"

σ=√Σ(x-x¯)²/n


s=√Σ(x-x¯)²/(n-1)

for technical reason we won't consider in this course, the sample 'variance" √Σ(x-x¯)² is deviation is divided by one less than the total number of data (n).

the "standard deviation" is one measure of the average distance each datum is a set is from the mean.

EXAMPLE: find the standard deviation of ages of people in our class.
a) without including the teacher MR. K.
σ=0.7556
x¯=17.61

b) including MR. K.
σ=4.6117
x¯=18.68

...so yeah thats where we left off in the dictionaries, I think tomorrow we'll be continuing on it though. So hopefully my notes are some kind of help you any of you. Thats what we did in first class. In second class well, we kind of went off topic on some infinitie thing? I was lost on that one so I'm not so sure. But then afterwards Mr. K showed us what a bell shaped curve is...but unfortunally I had forgotten my text book at school so I ain't able to decribe it to you...so maybe the next scribe can fill you guys all in about it or maybe we'll get it in our dictionaries tomorrow, we'll see!

And just another remind if you never got to see the chatbox earlier, tomorrow's scribe will be Steph. Okay! welps, later!!!






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