Topic 1: Mathematical Models and Topic 2: Location

mathematical model=simplification of real world situation
numerical data- quantitative; non numerical data- qualitative
continuous variable takes any value in given range, discrete can only take specific values

GROUPED DATA- useful to group data when in large amount
continuous data can be shown in more than one way,
eg. class weight= 31-40, class boundary=30.5 - 40.5, class width=10(40.5-30.5)

MEAN- find mean of 3, 10, 15, 7, 8= 43/8= 8.6
*now add 3 to all values and find mean* = 58/5 = 11.6
---11.6 = 8.6+ 3---
THIS IS CALLED CODING - makes values easier to work with !!
eg. number b is subtracted/added from each value, then mean is same w b added/subtracted
also works with division+multiplication!!
eg x=10y +50
if x =60, then y=60-50 / 10 = 1
(code all data and work out mean of y, then use coding to find mean of x)

Topic 3: Measures of Dispersion

STANDARD DEVIATION: essentially, SD is measure of how close values are to the mean
3 commonly used measures of spread: the range, IQR, standard deviation
based on all values of data- **v sensitive to outliers**
variance= (standard deviation)²
VARIANCE= E(x1-mean)squared / n OR Exi sq/n -(mean)sq
*******SD= sqr root (variance)

IN MOST DISTRIBUTIONS 67% data lie within 1 sd from mean, most in 2 sd. Values that lie >2 sd from mean are considered OUTLIERS - should be treated carefully -

MEAN + STANDARD DEVIATION
if you add/ subtract c to each piece of data, sd remains unchanged.
if you multiply/ divide every value by c then the sd is multiplied/ divided by c
eg, data set coded by x=y x 10- standard deviation of y= 1.41,
***therefore sd of x = 1.41 x 10 = 14.17

Topic 4: Representation of Data

QUARTILES AND BOX PLOTS- ** smaller the range, more consistent the data is**

data that is abnormally small/ large is classified as an OUTLIER. - less than LQ- 1.5 x IQR
more than UQ +1.5 x IQR
SHAPES OF DISTRIBUTION:
symmetrical/ no correlation IF Q2-Q1= Q3-Q2
positively skewed if Q2 - Q1 Q3 - Q2
negatively skewed if Q2 - Q1 > Q3 - Q2

HISTOGRAMS: used to display grouped continuous data, important points to remember:
*Area of each bar in histogram should be in proportion to the frequency
*when class width not all equal, proportional areas can be achieved by plotting frequency densities on vertical areas where
FREQUENCY DENSITY = FREQUENCY / CLASS WIDTH
rules for plotting histogram:
1.plot frequency densities on y axis 2. choose sensible scales 3. label both axis 4. give it a title!
AREA IS PROPORTIONAL TO FREQUENCY
A= K x F

Topic 5: Probability

possible things that can happen are called outcomes. eg outcome of throwing coin= heads/ tails
---->outcomes can be shown by: list/ sample space/ tree diagram
for equally likely outcomes the probability of event X occurring is P(x)= number of possible outcomes/ total number of outcomes
Eg. p of picking vowel from 'PROBABILITY' = 4/11
*****************************************
when outcomes not equally likely we can use relative frequency to estimate probabilities
data taken from experiment/ observation
Eg, coin thrown 50 times + lands heads 30 times, so P(tails) = 20/50 OR 2/5
***************************************************************
SAMPLE SPACE
EG. P(more than 5)= 26/36
2. P(less than 10) = 30/36

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Edexcel mathematics STATISTICS

STATISTICS 1