Mathematics AA SL IB Diploma Program - Topic 4: Statistics and Probability

" "" "


statistics ranch upgoteabilibijii
key statistical concepts

②
Population : an entire collection of individuals about which we want to draw conclusions .




②
Census : the collection of information from the whole population .




②
Sample : a subset of the population which should .




②
Survey : the collection of
information from a sample .




②
Data : information about individuals in a population .




②
Categorical variable ( qualitative) : describes a particular quality / characteristic which can be divided into categories .




②
Numerical variable ( quantitative) : describes a characteristic which has a numerical value which can be counted or measured .




Discrete numerical variable : exact number values → result of counting .




Continuous variable : values within certain result of measuring
→
a
range .




②
Parameter numerical quantity measuring aspect of the
:
a some population .




②
Statistic quantity calculated from the data gathered
:

from a sample → to estimate a
parameter .




②
Distribution the pattern of :
variation of data .




②
Outliers : data values that are either much
larger or much smaller than the
general body of data .




Frequency Tables

, Display of numerical data Histogram →
group variables

②
Column used to display discrete numerical variables
graphs are .




②
When data is recorded for continuous variable the data
a a
frequency histogram is used to display .




Exercise 23A


2. a. continuous variable .




b. Time 1min) Tally

0-9 1*1


10-19 1111/11*11*1

20-29 1*1111/111

30-39 111×1111

40 -49 111T I



c. positively skewed .




d. modal class : 10 -19min
Traveling time .




Measuring the center of data -
central tendency
Model discrete ) 1 Modal class ( continuous) : most frequently occurring value in the dataset .




Mean : statistical the arithmetic sum of all data values
name for average . mean =
the number of all data values
2 outliers use when
sy metrical
dataset present !
Median : middle value of an ordered dataset .
median = ntl
2




Exercise 2313.1

2. a. Mean dataset A : 6.46 b. Median data set A : 7 . c. The mean of dataset A is less than the mean of data set B.


Mean dataset B 6.85 : Median data set B : 7 .
since the Max value in dataset A is lower than the max value of

data set B.


d. The medians are the same for both datasets since 7- is


the middle value of the ordered dataset .

, Thursday ,
7- October


Standard Deviation 6)
On an how close are the individual values
average ,




from the mean .




Variance 104

standard deviation squared



Example :




X X -

µ (x -
Mi x x -

µ (x -
up
A. 1 1 3 5 5 µ :3 6=1.79

2 I 1
4
-
1 -
2 4
B. 2 2 3 4 µ :3 6=0.894

2 -
I 1 2 -
I 1
C. 1 2 3 4 5 µ :3 6=1.41

3 0 0 3 0 0


4 I 1 4 1 1

4 1 1 5 2 4



If = 0.894
f¥= 0.894




Exercises :




II. a. Mean
selling price : $163770 .




Median selling price : 127/600,729/500,131-400 ,

-32400,14-6400%-48000,16*00>19-2500,21+000,256-400
=
$147200 .




b. i. mean .




ii. median .




Home


12 . 21=15 List & spreadsheets → enter


3t0tatat4tat6tat3
13 .

µ=4 In A → list data points
9
InB→ list
frequency
36=3+0 tata +4+9+6 + a +3 Menu → 4( stats )


✗ = 5 4.2


16 Mean .
= median -_ 12 7- +9+111-13+14 +17+19+2/+12=12 1 Variable / 2 variable

9
n=9 21=6 =
name variables .




✗ → A


Mean Of
f- ✗
frequency distribution :
µ=
f-